What is the Greatest Common Factor of 17969 and 17980?

Greatest common factor (GCF) of 17969 and 17980 is 1.

GCF(17969,17980) = 1

We will now calculate the prime factors of 17969 and 17980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17969 and 17980.

How to find the GCF of 17969 and 17980?

We will first find the prime factorization of 17969 and 17980. After we will calculate the factors of 17969 and 17980 and find the biggest common factor number .

Step-1: Prime Factorization of 17969

Prime factors of 17969 are 7, 17, 151. Prime factorization of 17969 in exponential form is:

17969 = 7¹ × 17¹ × 151¹

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 17969

List of positive integer factors of 17969 that divides 17969 without a remainder.

1, 7, 17, 119, 151, 1057, 2567

Step-4: Factors of 17980

List of positive integer factors of 17980 that divides 17969 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 17969 and 17980. The biggest common factor number is the GCF number.
So the greatest common factor 17969 and 17980 is 1.

Also check out the Least Common Multiple of 17969 and 17980