What is the Greatest Common Factor of 75390 and 75400?

Greatest common factor (GCF) of 75390 and 75400 is 10.

GCF(75390,75400) = 10

We will now calculate the prime factors of 75390 and 75400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75390 and 75400.

How to find the GCF of 75390 and 75400?

We will first find the prime factorization of 75390 and 75400. After we will calculate the factors of 75390 and 75400 and find the biggest common factor number .

Step-1: Prime Factorization of 75390

Prime factors of 75390 are 2, 3, 5, 7, 359. Prime factorization of 75390 in exponential form is:

75390 = 2¹ × 3¹ × 5¹ × 7¹ × 359¹

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 75390

List of positive integer factors of 75390 that divides 75390 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 359, 718, 1077, 1795, 2154, 2513, 3590, 5026, 5385, 7539, 10770, 12565, 15078, 25130, 37695

Step-4: Factors of 75400

List of positive integer factors of 75400 that divides 75390 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 75390 and 75400. The biggest common factor number is the GCF number.
So the greatest common factor 75390 and 75400 is 10.

Also check out the Least Common Multiple of 75390 and 75400