What is the Greatest Common Factor of 75168 and 75186?

Greatest common factor (GCF) of 75168 and 75186 is 18.

GCF(75168,75186) = 18

We will now calculate the prime factors of 75168 and 75186, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75168 and 75186.

How to find the GCF of 75168 and 75186?

We will first find the prime factorization of 75168 and 75186. After we will calculate the factors of 75168 and 75186 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75186

Prime factors of 75186 are 2, 3, 4177. Prime factorization of 75186 in exponential form is:

75186 = 2¹ × 3² × 4177¹

Step-3: Factors of 75168

List of positive integer factors of 75168 that divides 75168 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

Step-4: Factors of 75186

List of positive integer factors of 75186 that divides 75168 without a remainder.

1, 2, 3, 6, 9, 18, 4177, 8354, 12531, 25062, 37593

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75168 and 75186. The biggest common factor number is the GCF number.
So the greatest common factor 75168 and 75186 is 18.

Also check out the Least Common Multiple of 75168 and 75186