What is the Greatest Common Factor of 17500 and 17514?

Greatest common factor (GCF) of 17500 and 17514 is 14.

GCF(17500,17514) = 14

We will now calculate the prime factors of 17500 and 17514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17500 and 17514.

How to find the GCF of 17500 and 17514?

We will first find the prime factorization of 17500 and 17514. After we will calculate the factors of 17500 and 17514 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 17514

Prime factors of 17514 are 2, 3, 7, 139. Prime factorization of 17514 in exponential form is:

17514 = 2¹ × 3² × 7¹ × 139¹

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 17514

List of positive integer factors of 17514 that divides 17500 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 139, 278, 417, 834, 973, 1251, 1946, 2502, 2919, 5838, 8757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17500 and 17514. The biggest common factor number is the GCF number.
So the greatest common factor 17500 and 17514 is 14.

Also check out the Least Common Multiple of 17500 and 17514