What is the Greatest Common Factor of 510 and 525?

Greatest common factor (GCF) of 510 and 525 is 15.

GCF(510,525) = 15

We will now calculate the prime factors of 510 and 525, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 510 and 525.

How to find the GCF of 510 and 525?

We will first find the prime factorization of 510 and 525. After we will calculate the factors of 510 and 525 and find the biggest common factor number .

Step-1: Prime Factorization of 510

Prime factors of 510 are 2, 3, 5, 17. Prime factorization of 510 in exponential form is:

510 = 2¹ × 3¹ × 5¹ × 17¹

Step-2: 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-3: Factors of 510

List of positive integer factors of 510 that divides 510 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255

Step-4: Factors of 525

List of positive integer factors of 525 that divides 510 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 510 and 525. The biggest common factor number is the GCF number.
So the greatest common factor 510 and 525 is 15.

Also check out the Least Common Multiple of 510 and 525