What is the Greatest Common Factor of 34971 and 34986?

Greatest common factor (GCF) of 34971 and 34986 is 3.

GCF(34971,34986) = 3

We will now calculate the prime factors of 34971 and 34986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34971 and 34986.

How to find the GCF of 34971 and 34986?

We will first find the prime factorization of 34971 and 34986. After we will calculate the factors of 34971 and 34986 and find the biggest common factor number .

Step-1: Prime Factorization of 34971

Prime factors of 34971 are 3, 11657. Prime factorization of 34971 in exponential form is:

34971 = 3¹ × 11657¹

Step-2: Prime Factorization of 34986

Prime factors of 34986 are 2, 3, 7, 17. Prime factorization of 34986 in exponential form is:

34986 = 2¹ × 3¹ × 7³ × 17¹

Step-3: Factors of 34971

List of positive integer factors of 34971 that divides 34971 without a remainder.

1, 3, 11657

Step-4: Factors of 34986

List of positive integer factors of 34986 that divides 34971 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 49, 51, 98, 102, 119, 147, 238, 294, 343, 357, 686, 714, 833, 1029, 1666, 2058, 2499, 4998, 5831, 11662, 17493

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34971 and 34986. The biggest common factor number is the GCF number.
So the greatest common factor 34971 and 34986 is 3.

Also check out the Least Common Multiple of 34971 and 34986