What is the Greatest Common Factor of 7500 and 7505?

Greatest common factor (GCF) of 7500 and 7505 is 5.

GCF(7500,7505) = 5

We will now calculate the prime factors of 7500 and 7505, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7500 and 7505.

How to find the GCF of 7500 and 7505?

We will first find the prime factorization of 7500 and 7505. After we will calculate the factors of 7500 and 7505 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 7505

Prime factors of 7505 are 5, 19, 79. Prime factorization of 7505 in exponential form is:

7505 = 5¹ × 19¹ × 79¹

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 7505

List of positive integer factors of 7505 that divides 7500 without a remainder.

1, 5, 19, 79, 95, 395, 1501

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7500 and 7505. The biggest common factor number is the GCF number.
So the greatest common factor 7500 and 7505 is 5.

Also check out the Least Common Multiple of 7500 and 7505