What is the Greatest Common Factor of 17507 and 17514?

Greatest common factor (GCF) of 17507 and 17514 is 7.

GCF(17507,17514) = 7

We will now calculate the prime factors of 17507 and 17514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17507 and 17514.

How to find the GCF of 17507 and 17514?

We will first find the prime factorization of 17507 and 17514. After we will calculate the factors of 17507 and 17514 and find the biggest common factor number .

Step-1: Prime Factorization of 17507

Prime factors of 17507 are 7, 41, 61. Prime factorization of 17507 in exponential form is:

17507 = 7¹ × 41¹ × 61¹

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 17507

List of positive integer factors of 17507 that divides 17507 without a remainder.

1, 7, 41, 61, 287, 427, 2501

Step-4: Factors of 17514

List of positive integer factors of 17514 that divides 17507 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 17507 and 17514. The biggest common factor number is the GCF number.
So the greatest common factor 17507 and 17514 is 7.

Also check out the Least Common Multiple of 17507 and 17514