What is the Greatest Common Factor of 34612 and 34629?

Greatest common factor (GCF) of 34612 and 34629 is 17.

GCF(34612,34629) = 17

We will now calculate the prime factors of 34612 and 34629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34612 and 34629.

How to find the GCF of 34612 and 34629?

We will first find the prime factorization of 34612 and 34629. After we will calculate the factors of 34612 and 34629 and find the biggest common factor number .

Step-1: Prime Factorization of 34612

Prime factors of 34612 are 2, 17, 509. Prime factorization of 34612 in exponential form is:

34612 = 2² × 17¹ × 509¹

Step-2: Prime Factorization of 34629

Prime factors of 34629 are 3, 7, 17, 97. Prime factorization of 34629 in exponential form is:

34629 = 3¹ × 7¹ × 17¹ × 97¹

Step-3: Factors of 34612

List of positive integer factors of 34612 that divides 34612 without a remainder.

1, 2, 4, 17, 34, 68, 509, 1018, 2036, 8653, 17306

Step-4: Factors of 34629

List of positive integer factors of 34629 that divides 34612 without a remainder.

1, 3, 7, 17, 21, 51, 97, 119, 291, 357, 679, 1649, 2037, 4947, 11543

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34612 and 34629. The biggest common factor number is the GCF number.
So the greatest common factor 34612 and 34629 is 17.

Also check out the Least Common Multiple of 34612 and 34629