What is the Greatest Common Factor of 1962 and 1978?

Greatest common factor (GCF) of 1962 and 1978 is 2.

GCF(1962,1978) = 2

We will now calculate the prime factors of 1962 and 1978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1962 and 1978.

How to find the GCF of 1962 and 1978?

We will first find the prime factorization of 1962 and 1978. After we will calculate the factors of 1962 and 1978 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1978

Prime factors of 1978 are 2, 23, 43. Prime factorization of 1978 in exponential form is:

1978 = 2¹ × 23¹ × 43¹

Step-3: Factors of 1962

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

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

Step-4: Factors of 1978

List of positive integer factors of 1978 that divides 1962 without a remainder.

1, 2, 23, 43, 46, 86, 989

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1962 and 1978. The biggest common factor number is the GCF number.
So the greatest common factor 1962 and 1978 is 2.

Also check out the Least Common Multiple of 1962 and 1978