What is the Greatest Common Factor of 1972 and 1976?

Greatest common factor (GCF) of 1972 and 1976 is 4.

GCF(1972,1976) = 4

We will now calculate the prime factors of 1972 and 1976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1972 and 1976.

How to find the GCF of 1972 and 1976?

We will first find the prime factorization of 1972 and 1976. After we will calculate the factors of 1972 and 1976 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 1976

Prime factors of 1976 are 2, 13, 19. Prime factorization of 1976 in exponential form is:

1976 = 2³ × 13¹ × 19¹

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 1976

List of positive integer factors of 1976 that divides 1972 without a remainder.

1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 247, 494, 988

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1972 and 1976. The biggest common factor number is the GCF number.
So the greatest common factor 1972 and 1976 is 4.

Also check out the Least Common Multiple of 1972 and 1976