What is the Greatest Common Factor of 17975 and 17980?

Greatest common factor (GCF) of 17975 and 17980 is 5.

GCF(17975,17980) = 5

We will now calculate the prime factors of 17975 and 17980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17975 and 17980.

How to find the GCF of 17975 and 17980?

We will first find the prime factorization of 17975 and 17980. After we will calculate the factors of 17975 and 17980 and find the biggest common factor number .

Step-1: Prime Factorization of 17975

Prime factors of 17975 are 5, 719. Prime factorization of 17975 in exponential form is:

17975 = 5² × 719¹

Step-2: Prime Factorization of 17980

Prime factors of 17980 are 2, 5, 29, 31. Prime factorization of 17980 in exponential form is:

17980 = 2² × 5¹ × 29¹ × 31¹

Step-3: Factors of 17975

List of positive integer factors of 17975 that divides 17975 without a remainder.

1, 5, 25, 719, 3595

Step-4: Factors of 17980

List of positive integer factors of 17980 that divides 17975 without a remainder.

1, 2, 4, 5, 10, 20, 29, 31, 58, 62, 116, 124, 145, 155, 290, 310, 580, 620, 899, 1798, 3596, 4495, 8990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17975 and 17980. The biggest common factor number is the GCF number.
So the greatest common factor 17975 and 17980 is 5.

Also check out the Least Common Multiple of 17975 and 17980