What is the Greatest Common Factor of 7488 and 7500?

Greatest common factor (GCF) of 7488 and 7500 is 12.

GCF(7488,7500) = 12

We will now calculate the prime factors of 7488 and 7500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7488 and 7500.

How to find the GCF of 7488 and 7500?

We will first find the prime factorization of 7488 and 7500. After we will calculate the factors of 7488 and 7500 and find the biggest common factor number .

Step-1: Prime Factorization of 7488

Prime factors of 7488 are 2, 3, 13. Prime factorization of 7488 in exponential form is:

7488 = 2⁶ × 3² × 13¹

Step-2: 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-3: Factors of 7488

List of positive integer factors of 7488 that divides 7488 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 144, 156, 192, 208, 234, 288, 312, 416, 468, 576, 624, 832, 936, 1248, 1872, 2496, 3744

Step-4: Factors of 7500

List of positive integer factors of 7500 that divides 7488 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7488 and 7500. The biggest common factor number is the GCF number.
So the greatest common factor 7488 and 7500 is 12.

Also check out the Least Common Multiple of 7488 and 7500