What is the Greatest Common Factor of 17500 and 17504?

Greatest common factor (GCF) of 17500 and 17504 is 4.

GCF(17500,17504) = 4

We will now calculate the prime factors of 17500 and 17504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17500 and 17504.

How to find the GCF of 17500 and 17504?

We will first find the prime factorization of 17500 and 17504. After we will calculate the factors of 17500 and 17504 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17504

Prime factors of 17504 are 2, 547. Prime factorization of 17504 in exponential form is:

17504 = 2⁵ × 547¹

Step-3: Factors of 17500

List of positive integer factors of 17500 that divides 17500 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

Step-4: Factors of 17504

List of positive integer factors of 17504 that divides 17500 without a remainder.

1, 2, 4, 8, 16, 32, 547, 1094, 2188, 4376, 8752

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17500 and 17504. The biggest common factor number is the GCF number.
So the greatest common factor 17500 and 17504 is 4.

Also check out the Least Common Multiple of 17500 and 17504