What is the Greatest Common Factor of 17528 and 17535?

Greatest common factor (GCF) of 17528 and 17535 is 7.

GCF(17528,17535) = 7

We will now calculate the prime factors of 17528 and 17535, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17528 and 17535.

How to find the GCF of 17528 and 17535?

We will first find the prime factorization of 17528 and 17535. After we will calculate the factors of 17528 and 17535 and find the biggest common factor number .

Step-1: Prime Factorization of 17528

Prime factors of 17528 are 2, 7, 313. Prime factorization of 17528 in exponential form is:

17528 = 2³ × 7¹ × 313¹

Step-2: Prime Factorization of 17535

Prime factors of 17535 are 3, 5, 7, 167. Prime factorization of 17535 in exponential form is:

17535 = 3¹ × 5¹ × 7¹ × 167¹

Step-3: Factors of 17528

List of positive integer factors of 17528 that divides 17528 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 313, 626, 1252, 2191, 2504, 4382, 8764

Step-4: Factors of 17535

List of positive integer factors of 17535 that divides 17528 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 167, 501, 835, 1169, 2505, 3507, 5845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17528 and 17535. The biggest common factor number is the GCF number.
So the greatest common factor 17528 and 17535 is 7.

Also check out the Least Common Multiple of 17528 and 17535