What is the Greatest Common Factor of 17974 and 17986?

Greatest common factor (GCF) of 17974 and 17986 is 2.

GCF(17974,17986) = 2

We will now calculate the prime factors of 17974 and 17986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17974 and 17986.

How to find the GCF of 17974 and 17986?

We will first find the prime factorization of 17974 and 17986. After we will calculate the factors of 17974 and 17986 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 17986

Prime factors of 17986 are 2, 17, 23. Prime factorization of 17986 in exponential form is:

17986 = 2¹ × 17¹ × 23²

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 17986

List of positive integer factors of 17986 that divides 17974 without a remainder.

1, 2, 17, 23, 34, 46, 391, 529, 782, 1058, 8993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17974 and 17986. The biggest common factor number is the GCF number.
So the greatest common factor 17974 and 17986 is 2.

Also check out the Least Common Multiple of 17974 and 17986