What is the Greatest Common Factor of 34974 and 34991?

Greatest common factor (GCF) of 34974 and 34991 is 1.

GCF(34974,34991) = 1

We will now calculate the prime factors of 34974 and 34991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34974 and 34991.

How to find the GCF of 34974 and 34991?

We will first find the prime factorization of 34974 and 34991. After we will calculate the factors of 34974 and 34991 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 34991

Prime factors of 34991 are 11, 3181. Prime factorization of 34991 in exponential form is:

34991 = 11¹ × 3181¹

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 34991

List of positive integer factors of 34991 that divides 34974 without a remainder.

1, 11, 3181

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34974 and 34991. The biggest common factor number is the GCF number.
So the greatest common factor 34974 and 34991 is 1.

Also check out the Least Common Multiple of 34974 and 34991