What is the Greatest Common Factor of 525 and 538?

Greatest common factor (GCF) of 525 and 538 is 1.

GCF(525,538) = 1

We will now calculate the prime factors of 525 and 538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 525 and 538.

How to find the GCF of 525 and 538?

We will first find the prime factorization of 525 and 538. After we will calculate the factors of 525 and 538 and find the biggest common factor number .

Step-1: Prime Factorization of 525

Prime factors of 525 are 3, 5, 7. Prime factorization of 525 in exponential form is:

525 = 3¹ × 5² × 7¹

Step-2: Prime Factorization of 538

Prime factors of 538 are 2, 269. Prime factorization of 538 in exponential form is:

538 = 2¹ × 269¹

Step-3: Factors of 525

List of positive integer factors of 525 that divides 525 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175

Step-4: Factors of 538

List of positive integer factors of 538 that divides 525 without a remainder.

1, 2, 269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 525 and 538. The biggest common factor number is the GCF number.
So the greatest common factor 525 and 538 is 1.

Also check out the Least Common Multiple of 525 and 538