What is the Greatest Common Factor of 17500 and 17520?

Greatest common factor (GCF) of 17500 and 17520 is 20.

GCF(17500,17520) = 20

We will now calculate the prime factors of 17500 and 17520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17500 and 17520.

How to find the GCF of 17500 and 17520?

We will first find the prime factorization of 17500 and 17520. After we will calculate the factors of 17500 and 17520 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 17520

Prime factors of 17520 are 2, 3, 5, 73. Prime factorization of 17520 in exponential form is:

17520 = 2⁴ × 3¹ × 5¹ × 73¹

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 17520

List of positive integer factors of 17520 that divides 17500 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 73, 80, 120, 146, 219, 240, 292, 365, 438, 584, 730, 876, 1095, 1168, 1460, 1752, 2190, 2920, 3504, 4380, 5840, 8760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17500 and 17520. The biggest common factor number is the GCF number.
So the greatest common factor 17500 and 17520 is 20.

Also check out the Least Common Multiple of 17500 and 17520