What is the Greatest Common Factor of 17752 and 17759?

Greatest common factor (GCF) of 17752 and 17759 is 7.

GCF(17752,17759) = 7

We will now calculate the prime factors of 17752 and 17759, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17752 and 17759.

How to find the GCF of 17752 and 17759?

We will first find the prime factorization of 17752 and 17759. After we will calculate the factors of 17752 and 17759 and find the biggest common factor number .

Step-1: Prime Factorization of 17752

Prime factors of 17752 are 2, 7, 317. Prime factorization of 17752 in exponential form is:

17752 = 2³ × 7¹ × 317¹

Step-2: Prime Factorization of 17759

Prime factors of 17759 are 7, 43, 59. Prime factorization of 17759 in exponential form is:

17759 = 7¹ × 43¹ × 59¹

Step-3: Factors of 17752

List of positive integer factors of 17752 that divides 17752 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 317, 634, 1268, 2219, 2536, 4438, 8876

Step-4: Factors of 17759

List of positive integer factors of 17759 that divides 17752 without a remainder.

1, 7, 43, 59, 301, 413, 2537

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17752 and 17759. The biggest common factor number is the GCF number.
So the greatest common factor 17752 and 17759 is 7.

Also check out the Least Common Multiple of 17752 and 17759