What is the Greatest Common Factor of 1944 and 1962?

Greatest common factor (GCF) of 1944 and 1962 is 18.

GCF(1944,1962) = 18

We will now calculate the prime factors of 1944 and 1962, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1944 and 1962.

How to find the GCF of 1944 and 1962?

We will first find the prime factorization of 1944 and 1962. After we will calculate the factors of 1944 and 1962 and find the biggest common factor number .

Step-1: Prime Factorization of 1944

Prime factors of 1944 are 2, 3. Prime factorization of 1944 in exponential form is:

1944 = 2³ × 3⁵

Step-2: Prime Factorization of 1962

Prime factors of 1962 are 2, 3, 109. Prime factorization of 1962 in exponential form is:

1962 = 2¹ × 3² × 109¹

Step-3: Factors of 1944

List of positive integer factors of 1944 that divides 1944 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972

Step-4: Factors of 1962

List of positive integer factors of 1962 that divides 1944 without a remainder.

1, 2, 3, 6, 9, 18, 109, 218, 327, 654, 981

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1944 and 1962. The biggest common factor number is the GCF number.
So the greatest common factor 1944 and 1962 is 18.

Also check out the Least Common Multiple of 1944 and 1962