What is the Greatest Common Factor of 1500 and 1506?

Greatest common factor (GCF) of 1500 and 1506 is 6.

GCF(1500,1506) = 6

We will now calculate the prime factors of 1500 and 1506, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1506.

How to find the GCF of 1500 and 1506?

We will first find the prime factorization of 1500 and 1506. After we will calculate the factors of 1500 and 1506 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 1506

Prime factors of 1506 are 2, 3, 251. Prime factorization of 1506 in exponential form is:

1506 = 2¹ × 3¹ × 251¹

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 1506

List of positive integer factors of 1506 that divides 1500 without a remainder.

1, 2, 3, 6, 251, 502, 753

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1506. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1506 is 6.

Also check out the Least Common Multiple of 1500 and 1506