What is the Greatest Common Factor of 65380 and 65400?

Greatest common factor (GCF) of 65380 and 65400 is 20.

GCF(65380,65400) = 20

We will now calculate the prime factors of 65380 and 65400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65380 and 65400.

How to find the GCF of 65380 and 65400?

We will first find the prime factorization of 65380 and 65400. After we will calculate the factors of 65380 and 65400 and find the biggest common factor number .

Step-1: Prime Factorization of 65380

Prime factors of 65380 are 2, 5, 7, 467. Prime factorization of 65380 in exponential form is:

65380 = 2² × 5¹ × 7¹ × 467¹

Step-2: Prime Factorization of 65400

Prime factors of 65400 are 2, 3, 5, 109. Prime factorization of 65400 in exponential form is:

65400 = 2³ × 3¹ × 5² × 109¹

Step-3: Factors of 65380

List of positive integer factors of 65380 that divides 65380 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 467, 934, 1868, 2335, 3269, 4670, 6538, 9340, 13076, 16345, 32690

Step-4: Factors of 65400

List of positive integer factors of 65400 that divides 65380 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 109, 120, 150, 200, 218, 300, 327, 436, 545, 600, 654, 872, 1090, 1308, 1635, 2180, 2616, 2725, 3270, 4360, 5450, 6540, 8175, 10900, 13080, 16350, 21800, 32700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65380 and 65400. The biggest common factor number is the GCF number.
So the greatest common factor 65380 and 65400 is 20.

Also check out the Least Common Multiple of 65380 and 65400