What is the Greatest Common Factor of 3974 and 3984?

Greatest common factor (GCF) of 3974 and 3984 is 2.

GCF(3974,3984) = 2

We will now calculate the prime factors of 3974 and 3984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3974 and 3984.

How to find the GCF of 3974 and 3984?

We will first find the prime factorization of 3974 and 3984. After we will calculate the factors of 3974 and 3984 and find the biggest common factor number .

Step-1: Prime Factorization of 3974

Prime factors of 3974 are 2, 1987. Prime factorization of 3974 in exponential form is:

3974 = 2¹ × 1987¹

Step-2: 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-3: Factors of 3974

List of positive integer factors of 3974 that divides 3974 without a remainder.

1, 2, 1987

Step-4: Factors of 3984

List of positive integer factors of 3984 that divides 3974 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3974 and 3984. The biggest common factor number is the GCF number.
So the greatest common factor 3974 and 3984 is 2.

Also check out the Least Common Multiple of 3974 and 3984