Greatest Common Factor (GCF)

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

Front

How do you find the GCF of two numbers using prime factorization?

Back

1. Factor each number into its prime factors. 2. Identify the common prime factors. 3. Multiply the lowest powers of these common factors to find the GCF.

Front

What is the GCF of 54 and 72?

Back

The GCF of 54 and 72 is 18.

Front

What is the GCF of 18, 30, and 66?

Back

The GCF of 18, 30, and 66 is 6.

Front

How can the GCF be found using the Euclidean algorithm?

Back

1. Divide the larger number by the smaller number. 2. Take the remainder and divide the smaller number by this remainder. 3. Repeat until the remainder is 0. The last non-zero remainder is the GCF.

Front

What is the GCF of 14 and 63?

Back

The GCF of 14 and 63 is 7.

Front

What is the GCF of 22, 33, and 88?

Back

The GCF of 22, 33, and 88 is 11.

Front

What is the GCF of 34 and 51?

Back

The GCF of 34 and 51 is 17.

Front

Why is finding the GCF important in mathematics?

Back

Finding the GCF is important for simplifying fractions, solving problems involving ratios, and finding common denominators.

Front

Can the GCF of a set of numbers be larger than the smallest number in the set?

Back

No, the GCF cannot be larger than the smallest number in the set.