What is the Greatest Common Factor of 17964 and 17974?

Greatest common factor (GCF) of 17964 and 17974 is 2.

GCF(17964,17974) = 2

We will now calculate the prime factors of 17964 and 17974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17964 and 17974.

How to find the GCF of 17964 and 17974?

We will first find the prime factorization of 17964 and 17974. After we will calculate the factors of 17964 and 17974 and find the biggest common factor number .

Step-1: Prime Factorization of 17964

Prime factors of 17964 are 2, 3, 499. Prime factorization of 17964 in exponential form is:

17964 = 2² × 3² × 499¹

Step-2: 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-3: Factors of 17964

List of positive integer factors of 17964 that divides 17964 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 499, 998, 1497, 1996, 2994, 4491, 5988, 8982

Step-4: Factors of 17974

List of positive integer factors of 17974 that divides 17964 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17964 and 17974. The biggest common factor number is the GCF number.
So the greatest common factor 17964 and 17974 is 2.

Also check out the Least Common Multiple of 17964 and 17974