What is the Greatest Common Factor of 38972 and 38976?

Greatest common factor (GCF) of 38972 and 38976 is 4.

GCF(38972,38976) = 4

We will now calculate the prime factors of 38972 and 38976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38972 and 38976.

How to find the GCF of 38972 and 38976?

We will first find the prime factorization of 38972 and 38976. After we will calculate the factors of 38972 and 38976 and find the biggest common factor number .

Step-1: Prime Factorization of 38972

Prime factors of 38972 are 2, 9743. Prime factorization of 38972 in exponential form is:

38972 = 2² × 9743¹

Step-2: 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-3: Factors of 38972

List of positive integer factors of 38972 that divides 38972 without a remainder.

1, 2, 4, 9743, 19486

Step-4: Factors of 38976

List of positive integer factors of 38976 that divides 38972 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38972 and 38976. The biggest common factor number is the GCF number.
So the greatest common factor 38972 and 38976 is 4.

Also check out the Least Common Multiple of 38972 and 38976