What is the Greatest Common Factor of 75392 and 75400?

Greatest common factor (GCF) of 75392 and 75400 is 8.

GCF(75392,75400) = 8

We will now calculate the prime factors of 75392 and 75400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75392 and 75400.

How to find the GCF of 75392 and 75400?

We will first find the prime factorization of 75392 and 75400. After we will calculate the factors of 75392 and 75400 and find the biggest common factor number .

Step-1: Prime Factorization of 75392

Prime factors of 75392 are 2, 19, 31. Prime factorization of 75392 in exponential form is:

75392 = 2⁷ × 19¹ × 31¹

Step-2: Prime Factorization of 75400

Prime factors of 75400 are 2, 5, 13, 29. Prime factorization of 75400 in exponential form is:

75400 = 2³ × 5² × 13¹ × 29¹

Step-3: Factors of 75392

List of positive integer factors of 75392 that divides 75392 without a remainder.

1, 2, 4, 8, 16, 19, 31, 32, 38, 62, 64, 76, 124, 128, 152, 248, 304, 496, 589, 608, 992, 1178, 1216, 1984, 2356, 2432, 3968, 4712, 9424, 18848, 37696

Step-4: Factors of 75400

List of positive integer factors of 75400 that divides 75392 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 29, 40, 50, 52, 58, 65, 100, 104, 116, 130, 145, 200, 232, 260, 290, 325, 377, 520, 580, 650, 725, 754, 1160, 1300, 1450, 1508, 1885, 2600, 2900, 3016, 3770, 5800, 7540, 9425, 15080, 18850, 37700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75392 and 75400. The biggest common factor number is the GCF number.
So the greatest common factor 75392 and 75400 is 8.

Also check out the Least Common Multiple of 75392 and 75400