What is the Greatest Common Factor of 67500 and 67510?

Greatest common factor (GCF) of 67500 and 67510 is 10.

GCF(67500,67510) = 10

We will now calculate the prime factors of 67500 and 67510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67500 and 67510.

How to find the GCF of 67500 and 67510?

We will first find the prime factorization of 67500 and 67510. After we will calculate the factors of 67500 and 67510 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 67510

Prime factors of 67510 are 2, 5, 43, 157. Prime factorization of 67510 in exponential form is:

67510 = 2¹ × 5¹ × 43¹ × 157¹

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 67510

List of positive integer factors of 67510 that divides 67500 without a remainder.

1, 2, 5, 10, 43, 86, 157, 215, 314, 430, 785, 1570, 6751, 13502, 33755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67500 and 67510. The biggest common factor number is the GCF number.
So the greatest common factor 67500 and 67510 is 10.

Also check out the Least Common Multiple of 67500 and 67510