What is the Greatest Common Factor of 3480 and 3500?

Greatest common factor (GCF) of 3480 and 3500 is 20.

GCF(3480,3500) = 20

We will now calculate the prime factors of 3480 and 3500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3480 and 3500.

How to find the GCF of 3480 and 3500?

We will first find the prime factorization of 3480 and 3500. After we will calculate the factors of 3480 and 3500 and find the biggest common factor number .

Step-1: Prime Factorization of 3480

Prime factors of 3480 are 2, 3, 5, 29. Prime factorization of 3480 in exponential form is:

3480 = 2³ × 3¹ × 5¹ × 29¹

Step-2: Prime Factorization of 3500

Prime factors of 3500 are 2, 5, 7. Prime factorization of 3500 in exponential form is:

3500 = 2² × 5³ × 7¹

Step-3: Factors of 3480

List of positive integer factors of 3480 that divides 3480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 29, 30, 40, 58, 60, 87, 116, 120, 145, 174, 232, 290, 348, 435, 580, 696, 870, 1160, 1740

Step-4: Factors of 3500

List of positive integer factors of 3500 that divides 3480 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3480 and 3500. The biggest common factor number is the GCF number.
So the greatest common factor 3480 and 3500 is 20.

Also check out the Least Common Multiple of 3480 and 3500