Question

Please help find the greatest common factor for these two 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.

13. The prime factorization of 8 is 2 * 2 * 2. The prime factorization of 26 is 2 * 13. Looking at the prime factorizations, we can see that both of them have 2. That means that the GCF is 1 * 2 which is 2.

12. The prime factorization of 105 is 3 * 5 * 7. The prime factorization of -30 is -5 * 6. We see that the number shared 5. That means that the GCF is 5 * 1 or 5.