What is the Greatest Common Factor of 38976 and 38988?

Greatest common factor (GCF) of 38976 and 38988 is 12.

GCF(38976,38988) = 12

We will now calculate the prime factors of 38976 and 38988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38976 and 38988.

How to find the GCF of 38976 and 38988?

We will first find the prime factorization of 38976 and 38988. After we will calculate the factors of 38976 and 38988 and find the biggest common factor number .

Step-1: Prime Factorization of 38976

Prime factors of 38976 are 2, 3, 7, 29. Prime factorization of 38976 in exponential form is:

38976 = 2⁶ × 3¹ × 7¹ × 29¹

Step-2: Prime Factorization of 38988

Prime factors of 38988 are 2, 3, 19. Prime factorization of 38988 in exponential form is:

38988 = 2² × 3³ × 19²

Step-3: Factors of 38976

List of positive integer factors of 38976 that divides 38976 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 64, 84, 87, 96, 112, 116, 168, 174, 192, 203, 224, 232, 336, 348, 406, 448, 464, 609, 672, 696, 812, 928, 1218, 1344, 1392, 1624, 1856, 2436, 2784, 3248, 4872, 5568, 6496, 9744, 12992, 19488

Step-4: Factors of 38988

List of positive integer factors of 38988 that divides 38976 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 27, 36, 38, 54, 57, 76, 108, 114, 171, 228, 342, 361, 513, 684, 722, 1026, 1083, 1444, 2052, 2166, 3249, 4332, 6498, 9747, 12996, 19494

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38976 and 38988. The biggest common factor number is the GCF number.
So the greatest common factor 38976 and 38988 is 12.

Also check out the Least Common Multiple of 38976 and 38988