What is the Greatest Common Factor of 17980 and 17994?

Greatest common factor (GCF) of 17980 and 17994 is 2.

GCF(17980,17994) = 2

We will now calculate the prime factors of 17980 and 17994, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17980 and 17994.

How to find the GCF of 17980 and 17994?

We will first find the prime factorization of 17980 and 17994. After we will calculate the factors of 17980 and 17994 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17994

Prime factors of 17994 are 2, 3, 2999. Prime factorization of 17994 in exponential form is:

17994 = 2¹ × 3¹ × 2999¹

Step-3: Factors of 17980

List of positive integer factors of 17980 that divides 17980 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

Step-4: Factors of 17994

List of positive integer factors of 17994 that divides 17980 without a remainder.

1, 2, 3, 6, 2999, 5998, 8997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17980 and 17994. The biggest common factor number is the GCF number.
So the greatest common factor 17980 and 17994 is 2.

Also check out the Least Common Multiple of 17980 and 17994