What is the Greatest Common Factor of 37974 and 37984?

Greatest common factor (GCF) of 37974 and 37984 is 2.

GCF(37974,37984) = 2

We will now calculate the prime factors of 37974 and 37984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37974 and 37984.

How to find the GCF of 37974 and 37984?

We will first find the prime factorization of 37974 and 37984. After we will calculate the factors of 37974 and 37984 and find the biggest common factor number .

Step-1: Prime Factorization of 37974

Prime factors of 37974 are 2, 3, 6329. Prime factorization of 37974 in exponential form is:

37974 = 2¹ × 3¹ × 6329¹

Step-2: Prime Factorization of 37984

Prime factors of 37984 are 2, 1187. Prime factorization of 37984 in exponential form is:

37984 = 2⁵ × 1187¹

Step-3: Factors of 37974

List of positive integer factors of 37974 that divides 37974 without a remainder.

1, 2, 3, 6, 6329, 12658, 18987

Step-4: Factors of 37984

List of positive integer factors of 37984 that divides 37974 without a remainder.

1, 2, 4, 8, 16, 32, 1187, 2374, 4748, 9496, 18992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37974 and 37984. The biggest common factor number is the GCF number.
So the greatest common factor 37974 and 37984 is 2.

Also check out the Least Common Multiple of 37974 and 37984