Greatest Common Factor Solutions and Explanations for Lesson 11

To solve for the highest number that evenly divides two or more integers, start by listing all divisors of each number. Identify the largest number that appears in all lists. This approach helps you easily find the greatest divisor shared between the numbers.

For example, when comparing 24 and 36, the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The greatest number appearing in both lists is 12. This is the shared divisor you’re looking for.

Another method to determine the greatest common divisor is by using prime factorization. Factor both numbers into prime factors, then choose the smallest powers of the common primes. Multiply these primes to get the greatest common divisor.

For instance, for 24, the prime factors are 2 x 2 x 2 x 3, and for 36, the prime factors are 2 x 2 x 3 x 3. The common prime factors are 2 x 2 x 3, which multiply to give 12. Both methods will give you the same result, but understanding both is useful in different contexts.