What is the Greatest Common Factor of 34974 and 34978?

Greatest common factor (GCF) of 34974 and 34978 is 2.

GCF(34974,34978) = 2

We will now calculate the prime factors of 34974 and 34978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34974 and 34978.

How to find the GCF of 34974 and 34978?

We will first find the prime factorization of 34974 and 34978. After we will calculate the factors of 34974 and 34978 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 34978

Prime factors of 34978 are 2, 17489. Prime factorization of 34978 in exponential form is:

34978 = 2¹ × 17489¹

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 34978

List of positive integer factors of 34978 that divides 34974 without a remainder.

1, 2, 17489

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34974 and 34978. The biggest common factor number is the GCF number.
So the greatest common factor 34974 and 34978 is 2.

Also check out the Least Common Multiple of 34974 and 34978