What is the Greatest Common Factor of 972 and 986?

Greatest common factor (GCF) of 972 and 986 is 2.

GCF(972,986) = 2

We will now calculate the prime factors of 972 and 986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 972 and 986.

How to find the GCF of 972 and 986?

We will first find the prime factorization of 972 and 986. After we will calculate the factors of 972 and 986 and find the biggest common factor number .

Step-1: Prime Factorization of 972

Prime factors of 972 are 2, 3. Prime factorization of 972 in exponential form is:

972 = 2² × 3⁵

Step-2: Prime Factorization of 986

Prime factors of 986 are 2, 17, 29. Prime factorization of 986 in exponential form is:

986 = 2¹ × 17¹ × 29¹

Step-3: Factors of 972

List of positive integer factors of 972 that divides 972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486

Step-4: Factors of 986

List of positive integer factors of 986 that divides 972 without a remainder.

1, 2, 17, 29, 34, 58, 493

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 972 and 986. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 986 is 2.

Also check out the Least Common Multiple of 972 and 986