What is the Greatest Common Factor of 3984 and 4000?

Greatest common factor (GCF) of 3984 and 4000 is 16.

GCF(3984,4000) = 16

We will now calculate the prime factors of 3984 and 4000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3984 and 4000.

How to find the GCF of 3984 and 4000?

We will first find the prime factorization of 3984 and 4000. After we will calculate the factors of 3984 and 4000 and find the biggest common factor number .

Step-1: Prime Factorization of 3984

Prime factors of 3984 are 2, 3, 83. Prime factorization of 3984 in exponential form is:

3984 = 2⁴ × 3¹ × 83¹

Step-2: Prime Factorization of 4000

Prime factors of 4000 are 2, 5. Prime factorization of 4000 in exponential form is:

4000 = 2⁵ × 5³

Step-3: Factors of 3984

List of positive integer factors of 3984 that divides 3984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 83, 166, 249, 332, 498, 664, 996, 1328, 1992

Step-4: Factors of 4000

List of positive integer factors of 4000 that divides 3984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3984 and 4000. The biggest common factor number is the GCF number.
So the greatest common factor 3984 and 4000 is 16.

Also check out the Least Common Multiple of 3984 and 4000