Factoring Numbers

Erica Matulich

MTED 301

MW 8:00AM

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““Factors” are the numbers you Factors” are the numbers you multiply to get another number.multiply to get another number.

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Example: Factors of Example: Factors of 1515

33 and and 55, because , because 33 x x 55= = 1515

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Some numbers have more than Some numbers have more than one factorization one factorization

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Example: 12Example: 12 12= 1x 1212= 1x 12

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Example: 12Example: 12 12= 1x 1212= 1x 12 12= 2 x 612= 2 x 6

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Example: 12Example: 12 12= 1x 1212= 1x 12 12= 2 x 612= 2 x 6 12= 3 x 412= 3 x 4

Idea #2Idea #2

A number that can be factored A number that can be factored as 1 times itself is called “prime”as 1 times itself is called “prime”

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First few prime numbers are:First few prime numbers are:

2,3,5,7,11,132,3,5,7,11,13

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You most often want to find the "prime You most often want to find the "prime factorization" of a number.factorization" of a number.

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Meaning: you want to find the list of all the Meaning: you want to find the list of all the prime-number factors of a given number.prime-number factors of a given number.

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For instance, the prime factorization of 8 is For instance, the prime factorization of 8 is 2×2×22×2×2, not just ", not just "22".".

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Yes, 2 is the only factor, but you need three Yes, 2 is the only factor, but you need three copies of it to multiply back to 8.copies of it to multiply back to 8.

2 x 2 x 2 = 82 x 2 x 2 = 8

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Prime factorization includes ONLY the prime Prime factorization includes ONLY the prime factors, not any products of those factors.factors, not any products of those factors.

Idea #4Idea #4

Prime factorization includes ONLY the prime Prime factorization includes ONLY the prime factors, not any products of those factors.factors, not any products of those factors.

For example: For example:

2×2 = 42×2 = 4

Idea #4Idea #4

Prime factorization includes ONLY the prime Prime factorization includes ONLY the prime factors, not any products of those factors.factors, not any products of those factors.

For example: For example:

2×2 = 42×2 = 4

4 is a divisor of 84 is a divisor of 8

Idea #4Idea #4

Prime factorization includes ONLY the prime Prime factorization includes ONLY the prime factors, not any products of those factors.factors, not any products of those factors.

For example: For example:

2×2 = 42×2 = 4

4 is a divisor of 84 is a divisor of 8

4 is NOT in the PRIME factorization of 8.4 is NOT in the PRIME factorization of 8.

Idea #4Idea #4

Prime factorization includes ONLY the prime Prime factorization includes ONLY the prime factors, not any products of those factors.factors, not any products of those factors.

For example: For example:

2×2 = 42×2 = 4

4 is a divisor of 84 is a divisor of 8

4 is NOT in the PRIME factorization of 8.4 is NOT in the PRIME factorization of 8.

That is because 8 does NOT equalThat is because 8 does NOT equal 2×2×2×4!2×2×2×4!

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Example: The numberExample: The number

2424

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2424/ \/ \

2 2 1212 / \/ \ 22 66

/ \/ \ 22 33

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2 x 2 x 2 x 3=2 x 2 x 2 x 3=

2424

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Find the prime factorization of Find the prime factorization of

10501050

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10501050 / \/ \ 2 2 525 525 / \/ \

33 175 175 / \/ \ 55 35 35 / \/ \ 5 75 7

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Then the answer is:  Then the answer is: 

1050 1050 = 2 × 3 × 5 × 5 × 7= 2 × 3 × 5 × 5 × 7

The EndThe End

Hope you learned something new and are Hope you learned something new and are excited to factor numbers!!excited to factor numbers!!