What is the Greatest Common Factor of 1974 and 1984?

Greatest common factor (GCF) of 1974 and 1984 is 2.

GCF(1974,1984) = 2

We will now calculate the prime factors of 1974 and 1984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1974 and 1984.

How to find the GCF of 1974 and 1984?

We will first find the prime factorization of 1974 and 1984. After we will calculate the factors of 1974 and 1984 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 1984

Prime factors of 1984 are 2, 31. Prime factorization of 1984 in exponential form is:

1984 = 2⁶ × 31¹

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 1984

List of positive integer factors of 1984 that divides 1974 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1974 and 1984. The biggest common factor number is the GCF number.
So the greatest common factor 1974 and 1984 is 2.

Also check out the Least Common Multiple of 1974 and 1984