What is the Greatest Common Factor of 6480 and 6500?

Greatest common factor (GCF) of 6480 and 6500 is 20.

GCF(6480,6500) = 20

We will now calculate the prime factors of 6480 and 6500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6480 and 6500.

How to find the GCF of 6480 and 6500?

We will first find the prime factorization of 6480 and 6500. After we will calculate the factors of 6480 and 6500 and find the biggest common factor number .

Step-1: Prime Factorization of 6480

Prime factors of 6480 are 2, 3, 5. Prime factorization of 6480 in exponential form is:

6480 = 2⁴ × 3⁴ × 5¹

Step-2: Prime Factorization of 6500

Prime factors of 6500 are 2, 5, 13. Prime factorization of 6500 in exponential form is:

6500 = 2² × 5³ × 13¹

Step-3: Factors of 6480

List of positive integer factors of 6480 that divides 6480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 108, 120, 135, 144, 162, 180, 216, 240, 270, 324, 360, 405, 432, 540, 648, 720, 810, 1080, 1296, 1620, 2160, 3240

Step-4: Factors of 6500

List of positive integer factors of 6500 that divides 6480 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 125, 130, 250, 260, 325, 500, 650, 1300, 1625, 3250

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6480 and 6500. The biggest common factor number is the GCF number.
So the greatest common factor 6480 and 6500 is 20.

Also check out the Least Common Multiple of 6480 and 6500