What is the Greatest Common Factor of 67500 and 67515?

Greatest common factor (GCF) of 67500 and 67515 is 15.

GCF(67500,67515) = 15

We will now calculate the prime factors of 67500 and 67515, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67500 and 67515.

How to find the GCF of 67500 and 67515?

We will first find the prime factorization of 67500 and 67515. After we will calculate the factors of 67500 and 67515 and find the biggest common factor number .

Step-1: Prime Factorization of 67500

Prime factors of 67500 are 2, 3, 5. Prime factorization of 67500 in exponential form is:

67500 = 2² × 3³ × 5⁴

Step-2: Prime Factorization of 67515

Prime factors of 67515 are 3, 5, 7, 643. Prime factorization of 67515 in exponential form is:

67515 = 3¹ × 5¹ × 7¹ × 643¹

Step-3: Factors of 67500

List of positive integer factors of 67500 that divides 67500 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 625, 675, 750, 900, 1125, 1250, 1350, 1500, 1875, 2250, 2500, 2700, 3375, 3750, 4500, 5625, 6750, 7500, 11250, 13500, 16875, 22500, 33750

Step-4: Factors of 67515

List of positive integer factors of 67515 that divides 67500 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 643, 1929, 3215, 4501, 9645, 13503, 22505

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67500 and 67515. The biggest common factor number is the GCF number.
So the greatest common factor 67500 and 67515 is 15.

Also check out the Least Common Multiple of 67500 and 67515