What is the Greatest Common Factor of 75150 and 75168?

Greatest common factor (GCF) of 75150 and 75168 is 18.

GCF(75150,75168) = 18

We will now calculate the prime factors of 75150 and 75168, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75150 and 75168.

How to find the GCF of 75150 and 75168?

We will first find the prime factorization of 75150 and 75168. After we will calculate the factors of 75150 and 75168 and find the biggest common factor number .

Step-1: Prime Factorization of 75150

Prime factors of 75150 are 2, 3, 5, 167. Prime factorization of 75150 in exponential form is:

75150 = 2¹ × 3² × 5² × 167¹

Step-2: Prime Factorization of 75168

Prime factors of 75168 are 2, 3, 29. Prime factorization of 75168 in exponential form is:

75168 = 2⁵ × 3⁴ × 29¹

Step-3: Factors of 75150

List of positive integer factors of 75150 that divides 75150 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 167, 225, 334, 450, 501, 835, 1002, 1503, 1670, 2505, 3006, 4175, 5010, 7515, 8350, 12525, 15030, 25050, 37575

Step-4: Factors of 75168

List of positive integer factors of 75168 that divides 75150 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 29, 32, 36, 48, 54, 58, 72, 81, 87, 96, 108, 116, 144, 162, 174, 216, 232, 261, 288, 324, 348, 432, 464, 522, 648, 696, 783, 864, 928, 1044, 1296, 1392, 1566, 2088, 2349, 2592, 2784, 3132, 4176, 4698, 6264, 8352, 9396, 12528, 18792, 25056, 37584

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75150 and 75168. The biggest common factor number is the GCF number.
So the greatest common factor 75150 and 75168 is 18.

Also check out the Least Common Multiple of 75150 and 75168