What is the Greatest Common Factor of 75375 and 75384?

Greatest common factor (GCF) of 75375 and 75384 is 9.

GCF(75375,75384) = 9

We will now calculate the prime factors of 75375 and 75384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75375 and 75384.

How to find the GCF of 75375 and 75384?

We will first find the prime factorization of 75375 and 75384. After we will calculate the factors of 75375 and 75384 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75384

Prime factors of 75384 are 2, 3, 349. Prime factorization of 75384 in exponential form is:

75384 = 2³ × 3³ × 349¹

Step-3: Factors of 75375

List of positive integer factors of 75375 that divides 75375 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

Step-4: Factors of 75384

List of positive integer factors of 75384 that divides 75375 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 349, 698, 1047, 1396, 2094, 2792, 3141, 4188, 6282, 8376, 9423, 12564, 18846, 25128, 37692

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75375 and 75384. The biggest common factor number is the GCF number.
So the greatest common factor 75375 and 75384 is 9.

Also check out the Least Common Multiple of 75375 and 75384