What is the Greatest Common Factor of 53625 and 53640?

Greatest common factor (GCF) of 53625 and 53640 is 15.

GCF(53625,53640) = 15

We will now calculate the prime factors of 53625 and 53640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53625 and 53640.

How to find the GCF of 53625 and 53640?

We will first find the prime factorization of 53625 and 53640. After we will calculate the factors of 53625 and 53640 and find the biggest common factor number .

Step-1: Prime Factorization of 53625

Prime factors of 53625 are 3, 5, 11, 13. Prime factorization of 53625 in exponential form is:

53625 = 3¹ × 5³ × 11¹ × 13¹

Step-2: Prime Factorization of 53640

Prime factors of 53640 are 2, 3, 5, 149. Prime factorization of 53640 in exponential form is:

53640 = 2³ × 3² × 5¹ × 149¹

Step-3: Factors of 53625

List of positive integer factors of 53625 that divides 53625 without a remainder.

1, 3, 5, 11, 13, 15, 25, 33, 39, 55, 65, 75, 125, 143, 165, 195, 275, 325, 375, 429, 715, 825, 975, 1375, 1625, 2145, 3575, 4125, 4875, 10725, 17875

Step-4: Factors of 53640

List of positive integer factors of 53640 that divides 53625 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 149, 180, 298, 360, 447, 596, 745, 894, 1192, 1341, 1490, 1788, 2235, 2682, 2980, 3576, 4470, 5364, 5960, 6705, 8940, 10728, 13410, 17880, 26820

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53625 and 53640. The biggest common factor number is the GCF number.
So the greatest common factor 53625 and 53640 is 15.

Also check out the Least Common Multiple of 53625 and 53640