What is the Greatest Common Factor of 1974 and 1982?

Greatest common factor (GCF) of 1974 and 1982 is 2.

GCF(1974,1982) = 2

We will now calculate the prime factors of 1974 and 1982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1974 and 1982.

How to find the GCF of 1974 and 1982?

We will first find the prime factorization of 1974 and 1982. After we will calculate the factors of 1974 and 1982 and find the biggest common factor number .

Step-1: Prime Factorization of 1974

Prime factors of 1974 are 2, 3, 7, 47. Prime factorization of 1974 in exponential form is:

1974 = 2¹ × 3¹ × 7¹ × 47¹

Step-2: Prime Factorization of 1982

Prime factors of 1982 are 2, 991. Prime factorization of 1982 in exponential form is:

1982 = 2¹ × 991¹

Step-3: Factors of 1974

List of positive integer factors of 1974 that divides 1974 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987

Step-4: Factors of 1982

List of positive integer factors of 1982 that divides 1974 without a remainder.

1, 2, 991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1974 and 1982. The biggest common factor number is the GCF number.
So the greatest common factor 1974 and 1982 is 2.

Also check out the Least Common Multiple of 1974 and 1982