What is the Greatest Common Factor of 1972 and 1977?

Greatest common factor (GCF) of 1972 and 1977 is 1.

GCF(1972,1977) = 1

We will now calculate the prime factors of 1972 and 1977, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1972 and 1977.

How to find the GCF of 1972 and 1977?

We will first find the prime factorization of 1972 and 1977. After we will calculate the factors of 1972 and 1977 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 1977

Prime factors of 1977 are 3, 659. Prime factorization of 1977 in exponential form is:

1977 = 3¹ × 659¹

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 1977

List of positive integer factors of 1977 that divides 1972 without a remainder.

1, 3, 659

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1972 and 1977. The biggest common factor number is the GCF number.
So the greatest common factor 1972 and 1977 is 1.

Also check out the Least Common Multiple of 1972 and 1977