What is the Greatest Common Factor of 1500 and 1505?

Greatest common factor (GCF) of 1500 and 1505 is 5.

GCF(1500,1505) = 5

We will now calculate the prime factors of 1500 and 1505, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1505.

How to find the GCF of 1500 and 1505?

We will first find the prime factorization of 1500 and 1505. After we will calculate the factors of 1500 and 1505 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 1505

Prime factors of 1505 are 5, 7, 43. Prime factorization of 1505 in exponential form is:

1505 = 5¹ × 7¹ × 43¹

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 1505

List of positive integer factors of 1505 that divides 1500 without a remainder.

1, 5, 7, 35, 43, 215, 301

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1505. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1505 is 5.

Also check out the Least Common Multiple of 1500 and 1505