What is the Greatest Common Factor of 67974 and 67984?

Greatest common factor (GCF) of 67974 and 67984 is 2.

GCF(67974,67984) = 2

We will now calculate the prime factors of 67974 and 67984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67974 and 67984.

How to find the GCF of 67974 and 67984?

We will first find the prime factorization of 67974 and 67984. After we will calculate the factors of 67974 and 67984 and find the biggest common factor number .

Step-1: Prime Factorization of 67974

Prime factors of 67974 are 2, 3, 11329. Prime factorization of 67974 in exponential form is:

67974 = 2¹ × 3¹ × 11329¹

Step-2: Prime Factorization of 67984

Prime factors of 67984 are 2, 7, 607. Prime factorization of 67984 in exponential form is:

67984 = 2⁴ × 7¹ × 607¹

Step-3: Factors of 67974

List of positive integer factors of 67974 that divides 67974 without a remainder.

1, 2, 3, 6, 11329, 22658, 33987

Step-4: Factors of 67984

List of positive integer factors of 67984 that divides 67974 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 607, 1214, 2428, 4249, 4856, 8498, 9712, 16996, 33992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67974 and 67984. The biggest common factor number is the GCF number.
So the greatest common factor 67974 and 67984 is 2.

Also check out the Least Common Multiple of 67974 and 67984