What is the Greatest Common Factor of 6500 and 6510?

Greatest common factor (GCF) of 6500 and 6510 is 10.

GCF(6500,6510) = 10

We will now calculate the prime factors of 6500 and 6510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6500 and 6510.

How to find the GCF of 6500 and 6510?

We will first find the prime factorization of 6500 and 6510. After we will calculate the factors of 6500 and 6510 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 6510

Prime factors of 6510 are 2, 3, 5, 7, 31. Prime factorization of 6510 in exponential form is:

6510 = 2¹ × 3¹ × 5¹ × 7¹ × 31¹

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 6510

List of positive integer factors of 6510 that divides 6500 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 31, 35, 42, 62, 70, 93, 105, 155, 186, 210, 217, 310, 434, 465, 651, 930, 1085, 1302, 2170, 3255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6500 and 6510. The biggest common factor number is the GCF number.
So the greatest common factor 6500 and 6510 is 10.

Also check out the Least Common Multiple of 6500 and 6510