What is the Greatest Common Factor of 34974 and 34990?

Greatest common factor (GCF) of 34974 and 34990 is 2.

GCF(34974,34990) = 2

We will now calculate the prime factors of 34974 and 34990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34974 and 34990.

How to find the GCF of 34974 and 34990?

We will first find the prime factorization of 34974 and 34990. After we will calculate the factors of 34974 and 34990 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 34990

Prime factors of 34990 are 2, 5, 3499. Prime factorization of 34990 in exponential form is:

34990 = 2¹ × 5¹ × 3499¹

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 34990

List of positive integer factors of 34990 that divides 34974 without a remainder.

1, 2, 5, 10, 3499, 6998, 17495

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34974 and 34990. The biggest common factor number is the GCF number.
So the greatest common factor 34974 and 34990 is 2.

Also check out the Least Common Multiple of 34974 and 34990