Divisibility tests These are simple tricks to test what a number can be shared by. We are going to...
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Transcript of Divisibility tests These are simple tricks to test what a number can be shared by. We are going to...
![Page 1: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/1.jpg)
Divisibility tests
These are simple tricks to test what a number can be shared by .
We are going to learn tricks for testing if a number can be shared by 2, 3, 4, 5, 6, 8, 9, and multiples of 10.
![Page 2: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/2.jpg)
Divisibility tests
x x = 150
This is a typical SATs question that can be solved by divisibility tests.
Here we are asked to list 3 numbers that can be multiplied to make 150. Think about it. We will come back to this question after we learn our skills.
![Page 3: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/3.jpg)
Divisibility tests
Divisible by 2?
If a number is divisible by 2…
![Page 4: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/4.jpg)
Divisibility tests
Divisible by 2?
If a number is divisible by 2…
It ends with 2, 4, 6, 8, or 0
(in other words it’s an EVEN number.)
![Page 5: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/5.jpg)
Divisibility tests
Divisible by 3?
If a number is divisible by 3…
![Page 6: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/6.jpg)
Divisibility tests
Divisible by 3?
If a number is divisible by 3…
It’s digit sum is 3, 6, or 9.
The digit sum is when you add the digits in the number repeating until you get to 1 digit.
![Page 7: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/7.jpg)
Divisibility tests
Divisible by 3?
So the number 1467 has a digit sum of 9
1 + 4 + 6 + 7 = 18 then 1 + 8 = 9
So 1467 is divisible by 3.
![Page 8: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/8.jpg)
Divisibility tests
Divisible by 4?
If a number is divisible by 4…
![Page 9: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/9.jpg)
Divisibility tests
Divisible by 4?
If a number is divisible by 4…
If we half the number, and the result is even, then our number is divisible by 4.
![Page 10: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/10.jpg)
Divisibility tests
Divisible by 4?
If a number is divisible by 4…
If the last 2 digits of a number are divisible by 4, then our number is as well.
4 655 728 is divisible by 4 because 28 is divisible by 4.
![Page 11: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/11.jpg)
Divisibility tests
Divisible by 5?
If a number is divisible by 5…
![Page 12: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/12.jpg)
Divisibility tests
Divisible by 5?
If a number is divisible by 5…
It ends with a 5 or a 0.
5, 10, 15, 20, 25, 30, …
![Page 13: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/13.jpg)
Divisibility tests
Divisible by 6?
If a number is divisible by 6…
![Page 14: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/14.jpg)
Divisibility tests
Divisible by 6?
If a number is divisible by 6…
It passes the tests for both divisibility by 2 and divisibility by 3.
In other words – an EVEN number with digit sum 3, 6 or 9
![Page 15: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/15.jpg)
Divisibility tests
Divisible by 7?
If a number is divisible by 7…
![Page 16: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/16.jpg)
Divisibility tests
Divisible by 7?
If a number is divisible by 7…
It appears in the 7 times table!
Sorry! You’ll just have to learn it because there is no trick for 7s!
![Page 17: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/17.jpg)
Divisibility tests
Divisible by 8?
If a number is divisible by 8…
![Page 18: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/18.jpg)
Divisibility tests
Divisible by 8?
If a number is divisible by 8…
If you halve it, and halve it again, the result is an even number.
If the last 3 digits are divisible by 8, the whole number will be.
![Page 19: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/19.jpg)
Divisibility tests
Divisible by 8?
If a number is divisible by 8…
So 2, 560, 104 is divisible by 8 because 104 is divisible by 8.
( 104 ÷ 2 = 52 52 ÷ 2 = 26 26 is EVEN. )
![Page 20: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/20.jpg)
Divisibility tests
Divisible by 9?
If a number is divisible by 9…
![Page 21: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/21.jpg)
Divisibility tests
Divisible by 9?
If a number is divisible by 9…
It’s digit sum is 9
![Page 22: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/22.jpg)
Divisibility tests
Divisible by 9?
If a number is divisible by 9…
It’s digit sum is 9
This means it is also divisible by 3!
![Page 23: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/23.jpg)
Divisibility tests
Divisible by 10?
If a number is divisible by 10…
It ends in a 0
![Page 24: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/24.jpg)
Divisibility tests
Divisible by 10?
If a number is divisible by 10…
It ends in a 0
So these numbers are also divisible by 2 and 5
![Page 25: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/25.jpg)
Divisibility tests
Divisible by 100?
If a number is divisible by 100…
It ends in a 00
![Page 26: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/26.jpg)
Divisibility tests
Divisible by 1000?
If a number is divisible by 1000…
It ends in a 000
![Page 27: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/27.jpg)
Divisibility tests
Divisible by 1000?
If a number is divisible by 1000…
It ends in a 000
And so on…
![Page 28: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/28.jpg)
Divisibility tests
Divisible by …?
2: ends with 2, 4, 6, 8, or 0
3: digit sum is 3, 6, or 9
4: halve last 2 digits and the result is even
5: ends with 5 or 0
6: ends with 2, 4, 6, 8, or 0 AND digit sum is 3, 6, or 9
7: -
8: Halve the last 3 digits twice, and the result is even.
9: digit sum is 9
10: ends with 0
![Page 29: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/29.jpg)
Divisibility tests
x x = 150
Remember this question…
Test 150 to see what can go in the boxes.
![Page 30: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/30.jpg)
Divisibility tests
x x = 150
Remember this question…
150 is divisible by 2, 3, 5, 6, and 10 amongst other numbers (pick any one for the first box)
![Page 31: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/31.jpg)
Divisibility tests
x x = 150
Remember this question…
2
150 ÷ 2 = 75
![Page 32: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/32.jpg)
Divisibility tests
x x = 150
Remember this question…
2
These must multiply to make 75
![Page 33: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/33.jpg)
Divisibility tests
x x = 150
Remember this question…
2
Test 75 for divisibility
![Page 34: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/34.jpg)
Divisibility tests
x x = 150
Remember this question…
2
75 is divisible by 3 and 5 among others (pick either for second box).
![Page 35: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/35.jpg)
Divisibility tests
x x = 150
Remember this question…
2
75 ÷ 3 = 25
3
![Page 36: Divisibility tests These are simple tricks to test what a number can be shared by. We are going to learn tricks for testing if a number can be shared by.](https://reader034.fdocuments.in/reader034/viewer/2022051412/5515f02c550346d46f8b5369/html5/thumbnails/36.jpg)
Divisibility tests
x x = 150
Remember this question…
2
This is one solution. Can you think of others?
3 25