What is the Greatest Common Factor of 67974 and 67983?

Greatest common factor (GCF) of 67974 and 67983 is 3.

GCF(67974,67983) = 3

We will now calculate the prime factors of 67974 and 67983, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67974 and 67983.

How to find the GCF of 67974 and 67983?

We will first find the prime factorization of 67974 and 67983. After we will calculate the factors of 67974 and 67983 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 67983

Prime factors of 67983 are 3, 17, 31, 43. Prime factorization of 67983 in exponential form is:

67983 = 3¹ × 17¹ × 31¹ × 43¹

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 67983

List of positive integer factors of 67983 that divides 67974 without a remainder.

1, 3, 17, 31, 43, 51, 93, 129, 527, 731, 1333, 1581, 2193, 3999, 22661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67974 and 67983. The biggest common factor number is the GCF number.
So the greatest common factor 67974 and 67983 is 3.

Also check out the Least Common Multiple of 67974 and 67983