What is the Greatest Common Factor of 75360 and 75375?

Greatest common factor (GCF) of 75360 and 75375 is 15.

GCF(75360,75375) = 15

We will now calculate the prime factors of 75360 and 75375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75360 and 75375.

How to find the GCF of 75360 and 75375?

We will first find the prime factorization of 75360 and 75375. After we will calculate the factors of 75360 and 75375 and find the biggest common factor number .

Step-1: Prime Factorization of 75360

Prime factors of 75360 are 2, 3, 5, 157. Prime factorization of 75360 in exponential form is:

75360 = 2⁵ × 3¹ × 5¹ × 157¹

Step-2: Prime Factorization of 75375

Prime factors of 75375 are 3, 5, 67. Prime factorization of 75375 in exponential form is:

75375 = 3² × 5³ × 67¹

Step-3: Factors of 75360

List of positive integer factors of 75360 that divides 75360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 157, 160, 240, 314, 471, 480, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 5024, 6280, 7536, 9420, 12560, 15072, 18840, 25120, 37680

Step-4: Factors of 75375

List of positive integer factors of 75375 that divides 75360 without a remainder.

1, 3, 5, 9, 15, 25, 45, 67, 75, 125, 201, 225, 335, 375, 603, 1005, 1125, 1675, 3015, 5025, 8375, 15075, 25125

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75360 and 75375. The biggest common factor number is the GCF number.
So the greatest common factor 75360 and 75375 is 15.

Also check out the Least Common Multiple of 75360 and 75375