What is the Greatest Common Factor of 17514 and 17521?

Greatest common factor (GCF) of 17514 and 17521 is 7.

GCF(17514,17521) = 7

We will now calculate the prime factors of 17514 and 17521, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17514 and 17521.

How to find the GCF of 17514 and 17521?

We will first find the prime factorization of 17514 and 17521. After we will calculate the factors of 17514 and 17521 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17521

Prime factors of 17521 are 7, 2503. Prime factorization of 17521 in exponential form is:

17521 = 7¹ × 2503¹

Step-3: Factors of 17514

List of positive integer factors of 17514 that divides 17514 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

Step-4: Factors of 17521

List of positive integer factors of 17521 that divides 17514 without a remainder.

1, 7, 2503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17514 and 17521. The biggest common factor number is the GCF number.
So the greatest common factor 17514 and 17521 is 7.

Also check out the Least Common Multiple of 17514 and 17521