What is the Greatest Common Factor of 7504 and 7524?

Greatest common factor (GCF) of 7504 and 7524 is 4.

GCF(7504,7524) = 4

We will now calculate the prime factors of 7504 and 7524, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7504 and 7524.

How to find the GCF of 7504 and 7524?

We will first find the prime factorization of 7504 and 7524. After we will calculate the factors of 7504 and 7524 and find the biggest common factor number .

Step-1: Prime Factorization of 7504

Prime factors of 7504 are 2, 7, 67. Prime factorization of 7504 in exponential form is:

7504 = 2⁴ × 7¹ × 67¹

Step-2: Prime Factorization of 7524

Prime factors of 7524 are 2, 3, 11, 19. Prime factorization of 7524 in exponential form is:

7524 = 2² × 3² × 11¹ × 19¹

Step-3: Factors of 7504

List of positive integer factors of 7504 that divides 7504 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 67, 112, 134, 268, 469, 536, 938, 1072, 1876, 3752

Step-4: Factors of 7524

List of positive integer factors of 7524 that divides 7504 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 19, 22, 33, 36, 38, 44, 57, 66, 76, 99, 114, 132, 171, 198, 209, 228, 342, 396, 418, 627, 684, 836, 1254, 1881, 2508, 3762

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7504 and 7524. The biggest common factor number is the GCF number.
So the greatest common factor 7504 and 7524 is 4.

Also check out the Least Common Multiple of 7504 and 7524