What is the Greatest Common Factor of 34524 and 34538?

Greatest common factor (GCF) of 34524 and 34538 is 14.

GCF(34524,34538) = 14

We will now calculate the prime factors of 34524 and 34538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34524 and 34538.

How to find the GCF of 34524 and 34538?

We will first find the prime factorization of 34524 and 34538. After we will calculate the factors of 34524 and 34538 and find the biggest common factor number .

Step-1: Prime Factorization of 34524

Prime factors of 34524 are 2, 3, 7, 137. Prime factorization of 34524 in exponential form is:

34524 = 2² × 3² × 7¹ × 137¹

Step-2: Prime Factorization of 34538

Prime factors of 34538 are 2, 7, 2467. Prime factorization of 34538 in exponential form is:

34538 = 2¹ × 7¹ × 2467¹

Step-3: Factors of 34524

List of positive integer factors of 34524 that divides 34524 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 137, 252, 274, 411, 548, 822, 959, 1233, 1644, 1918, 2466, 2877, 3836, 4932, 5754, 8631, 11508, 17262

Step-4: Factors of 34538

List of positive integer factors of 34538 that divides 34524 without a remainder.

1, 2, 7, 14, 2467, 4934, 17269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34524 and 34538. The biggest common factor number is the GCF number.
So the greatest common factor 34524 and 34538 is 14.

Also check out the Least Common Multiple of 34524 and 34538