What is the Greatest Common Factor of 16974 and 16983?

Greatest common factor (GCF) of 16974 and 16983 is 9.

GCF(16974,16983) = 9

We will now calculate the prime factors of 16974 and 16983, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16974 and 16983.

How to find the GCF of 16974 and 16983?

We will first find the prime factorization of 16974 and 16983. After we will calculate the factors of 16974 and 16983 and find the biggest common factor number .

Step-1: Prime Factorization of 16974

Prime factors of 16974 are 2, 3, 23, 41. Prime factorization of 16974 in exponential form is:

16974 = 2¹ × 3² × 23¹ × 41¹

Step-2: Prime Factorization of 16983

Prime factors of 16983 are 3, 17, 37. Prime factorization of 16983 in exponential form is:

16983 = 3³ × 17¹ × 37¹

Step-3: Factors of 16974

List of positive integer factors of 16974 that divides 16974 without a remainder.

1, 2, 3, 6, 9, 18, 23, 41, 46, 69, 82, 123, 138, 207, 246, 369, 414, 738, 943, 1886, 2829, 5658, 8487

Step-4: Factors of 16983

List of positive integer factors of 16983 that divides 16974 without a remainder.

1, 3, 9, 17, 27, 37, 51, 111, 153, 333, 459, 629, 999, 1887, 5661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16974 and 16983. The biggest common factor number is the GCF number.
So the greatest common factor 16974 and 16983 is 9.

Also check out the Least Common Multiple of 16974 and 16983