What is the Greatest Common Factor of 17375 and 17380?

Greatest common factor (GCF) of 17375 and 17380 is 5.

GCF(17375,17380) = 5

We will now calculate the prime factors of 17375 and 17380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17375 and 17380.

How to find the GCF of 17375 and 17380?

We will first find the prime factorization of 17375 and 17380. After we will calculate the factors of 17375 and 17380 and find the biggest common factor number .

Step-1: Prime Factorization of 17375

Prime factors of 17375 are 5, 139. Prime factorization of 17375 in exponential form is:

17375 = 5³ × 139¹

Step-2: Prime Factorization of 17380

Prime factors of 17380 are 2, 5, 11, 79. Prime factorization of 17380 in exponential form is:

17380 = 2² × 5¹ × 11¹ × 79¹

Step-3: Factors of 17375

List of positive integer factors of 17375 that divides 17375 without a remainder.

1, 5, 25, 125, 139, 695, 3475

Step-4: Factors of 17380

List of positive integer factors of 17380 that divides 17375 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 79, 110, 158, 220, 316, 395, 790, 869, 1580, 1738, 3476, 4345, 8690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17375 and 17380. The biggest common factor number is the GCF number.
So the greatest common factor 17375 and 17380 is 5.

Also check out the Least Common Multiple of 17375 and 17380