factoring numbers
DESCRIPTION
Factoring Numbers. Erica Matulich MTED 301 MW 8:00AM. Idea #1. “Factors” are the numbers you multiply to get another number. Idea #1. Example: Factors of 15 3 and 5 , because 3 x 5 = 15. Idea #1. Some numbers have more than one factorization. Idea #1. Example: 12 12= 1x 12. - PowerPoint PPT PresentationTRANSCRIPT
Factoring Numbers
Erica Matulich
MTED 301
MW 8:00AM
Idea #1Idea #1
““Factors” are the numbers you Factors” are the numbers you multiply to get another number.multiply to get another number.
Idea #1Idea #1
Example: Factors of Example: Factors of 1515
33 and and 55, because , because 33 x x 55= = 1515
Idea #1Idea #1
Some numbers have more than Some numbers have more than one factorization one factorization
Idea #1Idea #1
Example: 12Example: 12 12= 1x 1212= 1x 12
Idea #1Idea #1
Example: 12Example: 12 12= 1x 1212= 1x 12 12= 2 x 612= 2 x 6
Idea #1Idea #1
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”
Idea #2Idea #2
First few prime numbers are:First few prime numbers are:
2,3,5,7,11,132,3,5,7,11,13
Idea #3Idea #3
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.
Idea #3Idea #3
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".".
Idea #3Idea #3
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
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.
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!
Idea #4Idea #4
Example: The numberExample: The number
2424
Idea #4Idea #4
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
Idea #4Idea #4
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
Idea #4Idea #4
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!!