Greatest Common Factor

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 12 and 15?

Back

The GCF of 12 and 15 is 3.

Front

What is the GCF of 24 and 36?

Back

The GCF of 24 and 36 is 12.

Front

What is the relationship between GCF and LCM (Least Common Multiple)?

Back

The product of the GCF and LCM of two numbers is equal to the product of the numbers themselves.

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 18 and 24?

Back

The GCF of 18 and 24 is 6.

Front

Can the GCF of two prime numbers be greater than 1?

Back

No, the GCF of two distinct prime numbers is always 1.

Front

What is the GCF of 100 and 75?

Back

The GCF of 100 and 75 is 25.

Front

How does the GCF relate to simplifying fractions?

Back

The GCF of the numerator and denominator can be used to simplify a fraction to its lowest terms.