What is the Greatest Common Factor of 75270 and 75288?

Greatest common factor (GCF) of 75270 and 75288 is 6.

GCF(75270,75288) = 6

We will now calculate the prime factors of 75270 and 75288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75270 and 75288.

How to find the GCF of 75270 and 75288?

We will first find the prime factorization of 75270 and 75288. After we will calculate the factors of 75270 and 75288 and find the biggest common factor number .

Step-1: Prime Factorization of 75270

Prime factors of 75270 are 2, 3, 5, 13, 193. Prime factorization of 75270 in exponential form is:

75270 = 2¹ × 3¹ × 5¹ × 13¹ × 193¹

Step-2: Prime Factorization of 75288

Prime factors of 75288 are 2, 3, 3137. Prime factorization of 75288 in exponential form is:

75288 = 2³ × 3¹ × 3137¹

Step-3: Factors of 75270

List of positive integer factors of 75270 that divides 75270 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 193, 195, 386, 390, 579, 965, 1158, 1930, 2509, 2895, 5018, 5790, 7527, 12545, 15054, 25090, 37635

Step-4: Factors of 75288

List of positive integer factors of 75288 that divides 75270 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 3137, 6274, 9411, 12548, 18822, 25096, 37644

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75270 and 75288. The biggest common factor number is the GCF number.
So the greatest common factor 75270 and 75288 is 6.

Also check out the Least Common Multiple of 75270 and 75288