Question

Please help me find the greatest common factor for these 2 problems..

Answer 1

A greatest common factor is the largest number that goes into two or more numbers (in this case two). To find the GCF of two numbers, we have to find the prime factorization (how to express a number as a product of prime numbers) and then see which numbers are common in both of the prime factorizations.

11. The prime factorization of 12 is 3 * 2 * 2. The prime factorization of 18 is 3 * 3 * 2. Looking at the prime factorizations, we can see that both of them have 3 and 2. That means that the GCF is 3 * 2 which is 6.

12. The prime factorization of 48 is 2 * 2 * 2 * 2 * 3. The prime factorization of 80 is 2 * 2 * 2 * 2 * 5. We see that the numbers shared are 2, 2, 2, and 2. That means that the GCF is 2 * 2 * 2 * 2 or 16.

Answer 2

Problem 11.

12 = 2^2 * 3

18 = 2 * 3^2

Common factors with lower exponent: 2, 3

GCF = 2 * 3 = 6

11. Answer: 6

Problem 12.

48 = 2^4 * 3

80 = 2^4 * 5

Common factors with lower exponent: 2^4

GCF = 2^4 = 16

12. Answer: 16