What is the Greatest Common Factor of 6300 and 6320?

Greatest common factor (GCF) of 6300 and 6320 is 20.

GCF(6300,6320) = 20

We will now calculate the prime factors of 6300 and 6320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6300 and 6320.

How to find the GCF of 6300 and 6320?

We will first find the prime factorization of 6300 and 6320. After we will calculate the factors of 6300 and 6320 and find the biggest common factor number .

Step-1: Prime Factorization of 6300

Prime factors of 6300 are 2, 3, 5, 7. Prime factorization of 6300 in exponential form is:

6300 = 2² × 3² × 5² × 7¹

Step-2: Prime Factorization of 6320

Prime factors of 6320 are 2, 5, 79. Prime factorization of 6320 in exponential form is:

6320 = 2⁴ × 5¹ × 79¹

Step-3: Factors of 6300

List of positive integer factors of 6300 that divides 6300 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150

Step-4: Factors of 6320

List of positive integer factors of 6320 that divides 6300 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 79, 80, 158, 316, 395, 632, 790, 1264, 1580, 3160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6300 and 6320. The biggest common factor number is the GCF number.
So the greatest common factor 6300 and 6320 is 20.

Also check out the Least Common Multiple of 6300 and 6320