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Can someone tell me what is the GCF of 180 & 54 By using prime factorization (tell me wht the prime factorization is too, and how u got there....) Thanks In Advance!!

P.S. First Right Answer WILL Be The Best Answer!!!!

2007-09-05 09:45:16 · 2 answers · asked by • LeeYo • 6 in Science & Mathematics Mathematics

2 answers

180 is an even number, so 2 (the smallest prime number)
will divide into it to give 90. 90 is also divisible by 2 to
give 45. The next highest prime that will divide into 45 is 3
to give 15. 15 is also divisible by 3 to give 5. And 5 is only
divisible by 5. Then do the same with 54.

180 = 2 * 2 * 3 * 3 * 5

54 = 2 * 3 * 3 * 3

GCF is the most number of common factors.

Answer : 2 * 3 * 3 = 18

2007-09-05 10:44:01 · answer #1 · answered by falzoon 7 · 1 0

Get the prime factorization of both numbers. If the two factorizations have a "match" (they both have a 3, so that is a "match") then you write that number to the side. When you are out of matches (there are no more numbers to try), then the matches = prime factorization of the GCF.

edit: written more formally...

You have two numbers a and b. The prime factorization of a is...

a = p1^a1 * p2^a2 * p3^a3 * ...

Similarly, b = p1^b1 * p2^b2 * p3^b3 * ...

The p's are the prime numbers 2, 3, 5, etc. and the a_n's and b_n's are just exponents; note that a_n or b_n could be 0.

GCF (a,b) = p1^min(a1,b1) * p2^min(a2,b2) *...

The GCF is the *minimum* of the indexed exponents, most of which will probably be 0.

LCF (a,b) = p1^max(a1,b1) * p2^max(a2,b2) *...

2007-09-05 16:54:48 · answer #2 · answered by Mathsorcerer 7 · 0 0

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