What is the Greatest Common Factor of 17974 and 17980?

Greatest common factor (GCF) of 17974 and 17980 is 2.

GCF(17974,17980) = 2

We will now calculate the prime factors of 17974 and 17980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17974 and 17980.

How to find the GCF of 17974 and 17980?

We will first find the prime factorization of 17974 and 17980. After we will calculate the factors of 17974 and 17980 and find the biggest common factor number .

Step-1: Prime Factorization of 17974

Prime factors of 17974 are 2, 11, 19, 43. Prime factorization of 17974 in exponential form is:

17974 = 2¹ × 11¹ × 19¹ × 43¹

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 17974

List of positive integer factors of 17974 that divides 17974 without a remainder.

1, 2, 11, 19, 22, 38, 43, 86, 209, 418, 473, 817, 946, 1634, 8987

Step-4: Factors of 17980

List of positive integer factors of 17980 that divides 17974 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 17974 and 17980. The biggest common factor number is the GCF number.
So the greatest common factor 17974 and 17980 is 2.

Also check out the Least Common Multiple of 17974 and 17980