What is the Greatest Common Factor of 1954 and 1964?

Greatest common factor (GCF) of 1954 and 1964 is 2.

GCF(1954,1964) = 2

We will now calculate the prime factors of 1954 and 1964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1954 and 1964.

How to find the GCF of 1954 and 1964?

We will first find the prime factorization of 1954 and 1964. After we will calculate the factors of 1954 and 1964 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 1964

Prime factors of 1964 are 2, 491. Prime factorization of 1964 in exponential form is:

1964 = 2² × 491¹

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 1964

List of positive integer factors of 1964 that divides 1954 without a remainder.

1, 2, 4, 491, 982

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1954 and 1964. The biggest common factor number is the GCF number.
So the greatest common factor 1954 and 1964 is 2.

Also check out the Least Common Multiple of 1954 and 1964