What is the Greatest Common Factor of 1500 and 1510?

Greatest common factor (GCF) of 1500 and 1510 is 10.

GCF(1500,1510) = 10

We will now calculate the prime factors of 1500 and 1510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1510.

How to find the GCF of 1500 and 1510?

We will first find the prime factorization of 1500 and 1510. After we will calculate the factors of 1500 and 1510 and find the biggest common factor number .

Step-1: Prime Factorization of 1500

Prime factors of 1500 are 2, 3, 5. Prime factorization of 1500 in exponential form is:

1500 = 2² × 3¹ × 5³

Step-2: Prime Factorization of 1510

Prime factors of 1510 are 2, 5, 151. Prime factorization of 1510 in exponential form is:

1510 = 2¹ × 5¹ × 151¹

Step-3: Factors of 1500

List of positive integer factors of 1500 that divides 1500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750

Step-4: Factors of 1510

List of positive integer factors of 1510 that divides 1500 without a remainder.

1, 2, 5, 10, 151, 302, 755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1510. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1510 is 10.

Also check out the Least Common Multiple of 1500 and 1510