What is the Greatest Common Factor of 17974 and 17993?

Greatest common factor (GCF) of 17974 and 17993 is 19.

GCF(17974,17993) = 19

We will now calculate the prime factors of 17974 and 17993, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17974 and 17993.

How to find the GCF of 17974 and 17993?

We will first find the prime factorization of 17974 and 17993. After we will calculate the factors of 17974 and 17993 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 17993

Prime factors of 17993 are 19, 947. Prime factorization of 17993 in exponential form is:

17993 = 19¹ × 947¹

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 17993

List of positive integer factors of 17993 that divides 17974 without a remainder.

1, 19, 947

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17974 and 17993. The biggest common factor number is the GCF number.
So the greatest common factor 17974 and 17993 is 19.

Also check out the Least Common Multiple of 17974 and 17993