What is the Greatest Common Factor of 1954 and 1972?

Greatest common factor (GCF) of 1954 and 1972 is 2.

GCF(1954,1972) = 2

We will now calculate the prime factors of 1954 and 1972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1954 and 1972.

How to find the GCF of 1954 and 1972?

We will first find the prime factorization of 1954 and 1972. After we will calculate the factors of 1954 and 1972 and find the biggest common factor number .

Step-1: Prime Factorization of 1954

Prime factors of 1954 are 2, 977. Prime factorization of 1954 in exponential form is:

1954 = 2¹ × 977¹

Step-2: 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-3: Factors of 1954

List of positive integer factors of 1954 that divides 1954 without a remainder.

1, 2, 977

Step-4: Factors of 1972

List of positive integer factors of 1972 that divides 1954 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1954 and 1972. The biggest common factor number is the GCF number.
So the greatest common factor 1954 and 1972 is 2.

Also check out the Least Common Multiple of 1954 and 1972