What is the Greatest Common Factor of 30966 and 30972?

Greatest common factor (GCF) of 30966 and 30972 is 6.

GCF(30966,30972) = 6

We will now calculate the prime factors of 30966 and 30972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30966 and 30972.

How to find the GCF of 30966 and 30972?

We will first find the prime factorization of 30966 and 30972. After we will calculate the factors of 30966 and 30972 and find the biggest common factor number .

Step-1: Prime Factorization of 30966

Prime factors of 30966 are 2, 3, 13, 397. Prime factorization of 30966 in exponential form is:

30966 = 2¹ × 3¹ × 13¹ × 397¹

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 30966

List of positive integer factors of 30966 that divides 30966 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 397, 794, 1191, 2382, 5161, 10322, 15483

Step-4: Factors of 30972

List of positive integer factors of 30972 that divides 30966 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 30966 and 30972. The biggest common factor number is the GCF number.
So the greatest common factor 30966 and 30972 is 6.

Also check out the Least Common Multiple of 30966 and 30972