What is the Greatest Common Factor of 39968 and 39972?

Greatest common factor (GCF) of 39968 and 39972 is 4.

GCF(39968,39972) = 4

We will now calculate the prime factors of 39968 and 39972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39968 and 39972.

How to find the GCF of 39968 and 39972?

We will first find the prime factorization of 39968 and 39972. After we will calculate the factors of 39968 and 39972 and find the biggest common factor number .

Step-1: Prime Factorization of 39968

Prime factors of 39968 are 2, 1249. Prime factorization of 39968 in exponential form is:

39968 = 2⁵ × 1249¹

Step-2: Prime Factorization of 39972

Prime factors of 39972 are 2, 3, 3331. Prime factorization of 39972 in exponential form is:

39972 = 2² × 3¹ × 3331¹

Step-3: Factors of 39968

List of positive integer factors of 39968 that divides 39968 without a remainder.

1, 2, 4, 8, 16, 32, 1249, 2498, 4996, 9992, 19984

Step-4: Factors of 39972

List of positive integer factors of 39972 that divides 39968 without a remainder.

1, 2, 3, 4, 6, 12, 3331, 6662, 9993, 13324, 19986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39968 and 39972. The biggest common factor number is the GCF number.
So the greatest common factor 39968 and 39972 is 4.

Also check out the Least Common Multiple of 39968 and 39972