What is the Greatest Common Factor of 17486 and 17500?

Greatest common factor (GCF) of 17486 and 17500 is 14.

GCF(17486,17500) = 14

We will now calculate the prime factors of 17486 and 17500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17486 and 17500.

How to find the GCF of 17486 and 17500?

We will first find the prime factorization of 17486 and 17500. After we will calculate the factors of 17486 and 17500 and find the biggest common factor number .

Step-1: Prime Factorization of 17486

Prime factors of 17486 are 2, 7, 1249. Prime factorization of 17486 in exponential form is:

17486 = 2¹ × 7¹ × 1249¹

Step-2: Prime Factorization of 17500

Prime factors of 17500 are 2, 5, 7. Prime factorization of 17500 in exponential form is:

17500 = 2² × 5⁴ × 7¹

Step-3: Factors of 17486

List of positive integer factors of 17486 that divides 17486 without a remainder.

1, 2, 7, 14, 1249, 2498, 8743

Step-4: Factors of 17500

List of positive integer factors of 17500 that divides 17486 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 625, 700, 875, 1250, 1750, 2500, 3500, 4375, 8750

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17486 and 17500. The biggest common factor number is the GCF number.
So the greatest common factor 17486 and 17500 is 14.

Also check out the Least Common Multiple of 17486 and 17500