What is the Greatest Common Factor of 53385 and 53400?

Greatest common factor (GCF) of 53385 and 53400 is 15.

GCF(53385,53400) = 15

We will now calculate the prime factors of 53385 and 53400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53385 and 53400.

How to find the GCF of 53385 and 53400?

We will first find the prime factorization of 53385 and 53400. After we will calculate the factors of 53385 and 53400 and find the biggest common factor number .

Step-1: Prime Factorization of 53385

Prime factors of 53385 are 3, 5, 3559. Prime factorization of 53385 in exponential form is:

53385 = 3¹ × 5¹ × 3559¹

Step-2: Prime Factorization of 53400

Prime factors of 53400 are 2, 3, 5, 89. Prime factorization of 53400 in exponential form is:

53400 = 2³ × 3¹ × 5² × 89¹

Step-3: Factors of 53385

List of positive integer factors of 53385 that divides 53385 without a remainder.

1, 3, 5, 15, 3559, 10677, 17795

Step-4: Factors of 53400

List of positive integer factors of 53400 that divides 53385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 89, 100, 120, 150, 178, 200, 267, 300, 356, 445, 534, 600, 712, 890, 1068, 1335, 1780, 2136, 2225, 2670, 3560, 4450, 5340, 6675, 8900, 10680, 13350, 17800, 26700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53385 and 53400. The biggest common factor number is the GCF number.
So the greatest common factor 53385 and 53400 is 15.

Also check out the Least Common Multiple of 53385 and 53400