What is the Greatest Common Factor of 53175 and 53184?

Greatest common factor (GCF) of 53175 and 53184 is 3.

GCF(53175,53184) = 3

We will now calculate the prime factors of 53175 and 53184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53175 and 53184.

How to find the GCF of 53175 and 53184?

We will first find the prime factorization of 53175 and 53184. After we will calculate the factors of 53175 and 53184 and find the biggest common factor number .

Step-1: Prime Factorization of 53175

Prime factors of 53175 are 3, 5, 709. Prime factorization of 53175 in exponential form is:

53175 = 3¹ × 5² × 709¹

Step-2: Prime Factorization of 53184

Prime factors of 53184 are 2, 3, 277. Prime factorization of 53184 in exponential form is:

53184 = 2⁶ × 3¹ × 277¹

Step-3: Factors of 53175

List of positive integer factors of 53175 that divides 53175 without a remainder.

1, 3, 5, 15, 25, 75, 709, 2127, 3545, 10635, 17725

Step-4: Factors of 53184

List of positive integer factors of 53184 that divides 53175 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 277, 554, 831, 1108, 1662, 2216, 3324, 4432, 6648, 8864, 13296, 17728, 26592

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53175 and 53184. The biggest common factor number is the GCF number.
So the greatest common factor 53175 and 53184 is 3.

Also check out the Least Common Multiple of 53175 and 53184