What is the Greatest Common Factor of 7500 and 7510?

Greatest common factor (GCF) of 7500 and 7510 is 10.

GCF(7500,7510) = 10

We will now calculate the prime factors of 7500 and 7510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7500 and 7510.

How to find the GCF of 7500 and 7510?

We will first find the prime factorization of 7500 and 7510. After we will calculate the factors of 7500 and 7510 and find the biggest common factor number .

Step-1: Prime Factorization of 7500

Prime factors of 7500 are 2, 3, 5. Prime factorization of 7500 in exponential form is:

7500 = 2² × 3¹ × 5⁴

Step-2: Prime Factorization of 7510

Prime factors of 7510 are 2, 5, 751. Prime factorization of 7510 in exponential form is:

7510 = 2¹ × 5¹ × 751¹

Step-3: Factors of 7500

List of positive integer factors of 7500 that divides 7500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 625, 750, 1250, 1500, 1875, 2500, 3750

Step-4: Factors of 7510

List of positive integer factors of 7510 that divides 7500 without a remainder.

1, 2, 5, 10, 751, 1502, 3755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7500 and 7510. The biggest common factor number is the GCF number.
So the greatest common factor 7500 and 7510 is 10.

Also check out the Least Common Multiple of 7500 and 7510