What is the Greatest Common Factor of 36972 and 36984?

Greatest common factor (GCF) of 36972 and 36984 is 12.

GCF(36972,36984) = 12

We will now calculate the prime factors of 36972 and 36984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36972 and 36984.

How to find the GCF of 36972 and 36984?

We will first find the prime factorization of 36972 and 36984. After we will calculate the factors of 36972 and 36984 and find the biggest common factor number .

Step-1: Prime Factorization of 36972

Prime factors of 36972 are 2, 3, 13, 79. Prime factorization of 36972 in exponential form is:

36972 = 2² × 3² × 13¹ × 79¹

Step-2: Prime Factorization of 36984

Prime factors of 36984 are 2, 3, 23, 67. Prime factorization of 36984 in exponential form is:

36984 = 2³ × 3¹ × 23¹ × 67¹

Step-3: Factors of 36972

List of positive integer factors of 36972 that divides 36972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 79, 117, 156, 158, 234, 237, 316, 468, 474, 711, 948, 1027, 1422, 2054, 2844, 3081, 4108, 6162, 9243, 12324, 18486

Step-4: Factors of 36984

List of positive integer factors of 36984 that divides 36972 without a remainder.

1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 67, 69, 92, 134, 138, 184, 201, 268, 276, 402, 536, 552, 804, 1541, 1608, 3082, 4623, 6164, 9246, 12328, 18492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36972 and 36984. The biggest common factor number is the GCF number.
So the greatest common factor 36972 and 36984 is 12.

Also check out the Least Common Multiple of 36972 and 36984