What is the Greatest Common Factor of 30964 and 30972?

Greatest common factor (GCF) of 30964 and 30972 is 4.

GCF(30964,30972) = 4

We will now calculate the prime factors of 30964 and 30972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30964 and 30972.

How to find the GCF of 30964 and 30972?

We will first find the prime factorization of 30964 and 30972. After we will calculate the factors of 30964 and 30972 and find the biggest common factor number .

Step-1: Prime Factorization of 30964

Prime factors of 30964 are 2, 7741. Prime factorization of 30964 in exponential form is:

30964 = 2² × 7741¹

Step-2: Prime Factorization of 30972

Prime factors of 30972 are 2, 3, 29, 89. Prime factorization of 30972 in exponential form is:

30972 = 2² × 3¹ × 29¹ × 89¹

Step-3: Factors of 30964

List of positive integer factors of 30964 that divides 30964 without a remainder.

1, 2, 4, 7741, 15482

Step-4: Factors of 30972

List of positive integer factors of 30972 that divides 30964 without a remainder.

1, 2, 3, 4, 6, 12, 29, 58, 87, 89, 116, 174, 178, 267, 348, 356, 534, 1068, 2581, 5162, 7743, 10324, 15486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30964 and 30972. The biggest common factor number is the GCF number.
So the greatest common factor 30964 and 30972 is 4.

Also check out the Least Common Multiple of 30964 and 30972