What is the Greatest Common Factor of 34974 and 34992?

Greatest common factor (GCF) of 34974 and 34992 is 18.

GCF(34974,34992) = 18

We will now calculate the prime factors of 34974 and 34992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34974 and 34992.

How to find the GCF of 34974 and 34992?

We will first find the prime factorization of 34974 and 34992. After we will calculate the factors of 34974 and 34992 and find the biggest common factor number .

Step-1: Prime Factorization of 34974

Prime factors of 34974 are 2, 3, 29, 67. Prime factorization of 34974 in exponential form is:

34974 = 2¹ × 3² × 29¹ × 67¹

Step-2: Prime Factorization of 34992

Prime factors of 34992 are 2, 3. Prime factorization of 34992 in exponential form is:

34992 = 2⁴ × 3⁷

Step-3: Factors of 34974

List of positive integer factors of 34974 that divides 34974 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 67, 87, 134, 174, 201, 261, 402, 522, 603, 1206, 1943, 3886, 5829, 11658, 17487

Step-4: Factors of 34992

List of positive integer factors of 34992 that divides 34974 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 243, 324, 432, 486, 648, 729, 972, 1296, 1458, 1944, 2187, 2916, 3888, 4374, 5832, 8748, 11664, 17496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34974 and 34992. The biggest common factor number is the GCF number.
So the greatest common factor 34974 and 34992 is 18.

Also check out the Least Common Multiple of 34974 and 34992