What is the Greatest Common Factor of 34638 and 34658?

Greatest common factor (GCF) of 34638 and 34658 is 2.

GCF(34638,34658) = 2

We will now calculate the prime factors of 34638 and 34658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34638 and 34658.

How to find the GCF of 34638 and 34658?

We will first find the prime factorization of 34638 and 34658. After we will calculate the factors of 34638 and 34658 and find the biggest common factor number .

Step-1: Prime Factorization of 34638

Prime factors of 34638 are 2, 3, 23, 251. Prime factorization of 34638 in exponential form is:

34638 = 2¹ × 3¹ × 23¹ × 251¹

Step-2: Prime Factorization of 34658

Prime factors of 34658 are 2, 13, 31, 43. Prime factorization of 34658 in exponential form is:

34658 = 2¹ × 13¹ × 31¹ × 43¹

Step-3: Factors of 34638

List of positive integer factors of 34638 that divides 34638 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 251, 502, 753, 1506, 5773, 11546, 17319

Step-4: Factors of 34658

List of positive integer factors of 34658 that divides 34638 without a remainder.

1, 2, 13, 26, 31, 43, 62, 86, 403, 559, 806, 1118, 1333, 2666, 17329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34638 and 34658. The biggest common factor number is the GCF number.
So the greatest common factor 34638 and 34658 is 2.

Also check out the Least Common Multiple of 34638 and 34658