What is the Greatest Common Factor of 52380 and 52400?

Greatest common factor (GCF) of 52380 and 52400 is 20.

GCF(52380,52400) = 20

We will now calculate the prime factors of 52380 and 52400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52380 and 52400.

How to find the GCF of 52380 and 52400?

We will first find the prime factorization of 52380 and 52400. After we will calculate the factors of 52380 and 52400 and find the biggest common factor number .

Step-1: Prime Factorization of 52380

Prime factors of 52380 are 2, 3, 5, 97. Prime factorization of 52380 in exponential form is:

52380 = 2² × 3³ × 5¹ × 97¹

Step-2: Prime Factorization of 52400

Prime factors of 52400 are 2, 5, 131. Prime factorization of 52400 in exponential form is:

52400 = 2⁴ × 5² × 131¹

Step-3: Factors of 52380

List of positive integer factors of 52380 that divides 52380 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 97, 108, 135, 180, 194, 270, 291, 388, 485, 540, 582, 873, 970, 1164, 1455, 1746, 1940, 2619, 2910, 3492, 4365, 5238, 5820, 8730, 10476, 13095, 17460, 26190

Step-4: Factors of 52400

List of positive integer factors of 52400 that divides 52380 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 131, 200, 262, 400, 524, 655, 1048, 1310, 2096, 2620, 3275, 5240, 6550, 10480, 13100, 26200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52380 and 52400. The biggest common factor number is the GCF number.
So the greatest common factor 52380 and 52400 is 20.

Also check out the Least Common Multiple of 52380 and 52400