What is the Greatest Common Factor of 1984 and 1996?

Greatest common factor (GCF) of 1984 and 1996 is 4.

GCF(1984,1996) = 4

We will now calculate the prime factors of 1984 and 1996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1984 and 1996.

How to find the GCF of 1984 and 1996?

We will first find the prime factorization of 1984 and 1996. After we will calculate the factors of 1984 and 1996 and find the biggest common factor number .

Step-1: Prime Factorization of 1984

Prime factors of 1984 are 2, 31. Prime factorization of 1984 in exponential form is:

1984 = 2⁶ × 31¹

Step-2: Prime Factorization of 1996

Prime factors of 1996 are 2, 499. Prime factorization of 1996 in exponential form is:

1996 = 2² × 499¹

Step-3: Factors of 1984

List of positive integer factors of 1984 that divides 1984 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992

Step-4: Factors of 1996

List of positive integer factors of 1996 that divides 1984 without a remainder.

1, 2, 4, 499, 998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1984 and 1996. The biggest common factor number is the GCF number.
So the greatest common factor 1984 and 1996 is 4.

Also check out the Least Common Multiple of 1984 and 1996