What is the Greatest Common Factor of 1972 and 1984?

Greatest common factor (GCF) of 1972 and 1984 is 4.

GCF(1972,1984) = 4

We will now calculate the prime factors of 1972 and 1984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1972 and 1984.

How to find the GCF of 1972 and 1984?

We will first find the prime factorization of 1972 and 1984. After we will calculate the factors of 1972 and 1984 and find the biggest common factor number .

Step-1: Prime Factorization of 1972

Prime factors of 1972 are 2, 17, 29. Prime factorization of 1972 in exponential form is:

1972 = 2² × 17¹ × 29¹

Step-2: Prime Factorization of 1984

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

1984 = 2⁶ × 31¹

Step-3: Factors of 1972

List of positive integer factors of 1972 that divides 1972 without a remainder.

1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986

Step-4: Factors of 1984

List of positive integer factors of 1984 that divides 1972 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1972 and 1984. The biggest common factor number is the GCF number.
So the greatest common factor 1972 and 1984 is 4.

Also check out the Least Common Multiple of 1972 and 1984