What is the Greatest Common Factor of 30972 and 30992?

Greatest common factor (GCF) of 30972 and 30992 is 4.

GCF(30972,30992) = 4

We will now calculate the prime factors of 30972 and 30992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30972 and 30992.

How to find the GCF of 30972 and 30992?

We will first find the prime factorization of 30972 and 30992. After we will calculate the factors of 30972 and 30992 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30992

Prime factors of 30992 are 2, 13, 149. Prime factorization of 30992 in exponential form is:

30992 = 2⁴ × 13¹ × 149¹

Step-3: Factors of 30972

List of positive integer factors of 30972 that divides 30972 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

Step-4: Factors of 30992

List of positive integer factors of 30992 that divides 30972 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 149, 208, 298, 596, 1192, 1937, 2384, 3874, 7748, 15496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30972 and 30992. The biggest common factor number is the GCF number.
So the greatest common factor 30972 and 30992 is 4.

Also check out the Least Common Multiple of 30972 and 30992