What is the Greatest Common Factor of 6500 and 6514?

Greatest common factor (GCF) of 6500 and 6514 is 2.

GCF(6500,6514) = 2

We will now calculate the prime factors of 6500 and 6514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6500 and 6514.

How to find the GCF of 6500 and 6514?

We will first find the prime factorization of 6500 and 6514. After we will calculate the factors of 6500 and 6514 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 6514

Prime factors of 6514 are 2, 3257. Prime factorization of 6514 in exponential form is:

6514 = 2¹ × 3257¹

Step-3: Factors of 6500

List of positive integer factors of 6500 that divides 6500 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

Step-4: Factors of 6514

List of positive integer factors of 6514 that divides 6500 without a remainder.

1, 2, 3257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6500 and 6514. The biggest common factor number is the GCF number.
So the greatest common factor 6500 and 6514 is 2.

Also check out the Least Common Multiple of 6500 and 6514