What is the Greatest Common Factor of 1480 and 1500?

Greatest common factor (GCF) of 1480 and 1500 is 20.

GCF(1480,1500) = 20

We will now calculate the prime factors of 1480 and 1500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1480 and 1500.

How to find the GCF of 1480 and 1500?

We will first find the prime factorization of 1480 and 1500. After we will calculate the factors of 1480 and 1500 and find the biggest common factor number .

Step-1: Prime Factorization of 1480

Prime factors of 1480 are 2, 5, 37. Prime factorization of 1480 in exponential form is:

1480 = 2³ × 5¹ × 37¹

Step-2: 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-3: Factors of 1480

List of positive integer factors of 1480 that divides 1480 without a remainder.

1, 2, 4, 5, 8, 10, 20, 37, 40, 74, 148, 185, 296, 370, 740

Step-4: Factors of 1500

List of positive integer factors of 1500 that divides 1480 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1480 and 1500. The biggest common factor number is the GCF number.
So the greatest common factor 1480 and 1500 is 20.

Also check out the Least Common Multiple of 1480 and 1500