What is the Greatest Common Factor of 966 and 974?

Greatest common factor (GCF) of 966 and 974 is 2.

GCF(966,974) = 2

We will now calculate the prime factors of 966 and 974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 966 and 974.

How to find the GCF of 966 and 974?

We will first find the prime factorization of 966 and 974. After we will calculate the factors of 966 and 974 and find the biggest common factor number .

Step-1: Prime Factorization of 966

Prime factors of 966 are 2, 3, 7, 23. Prime factorization of 966 in exponential form is:

966 = 2¹ × 3¹ × 7¹ × 23¹

Step-2: Prime Factorization of 974

Prime factors of 974 are 2, 487. Prime factorization of 974 in exponential form is:

974 = 2¹ × 487¹

Step-3: Factors of 966

List of positive integer factors of 966 that divides 966 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483

Step-4: Factors of 974

List of positive integer factors of 974 that divides 966 without a remainder.

1, 2, 487

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 966 and 974. The biggest common factor number is the GCF number.
So the greatest common factor 966 and 974 is 2.

Also check out the Least Common Multiple of 966 and 974