What is the Greatest Common Factor of 53625 and 53638?

Greatest common factor (GCF) of 53625 and 53638 is 13.

GCF(53625,53638) = 13

We will now calculate the prime factors of 53625 and 53638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53625 and 53638.

How to find the GCF of 53625 and 53638?

We will first find the prime factorization of 53625 and 53638. After we will calculate the factors of 53625 and 53638 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 53638

Prime factors of 53638 are 2, 13, 2063. Prime factorization of 53638 in exponential form is:

53638 = 2¹ × 13¹ × 2063¹

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 53638

List of positive integer factors of 53638 that divides 53625 without a remainder.

1, 2, 13, 26, 2063, 4126, 26819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53625 and 53638. The biggest common factor number is the GCF number.
So the greatest common factor 53625 and 53638 is 13.

Also check out the Least Common Multiple of 53625 and 53638