What is the Greatest Common Factor of 16974 and 16982?

Greatest common factor (GCF) of 16974 and 16982 is 2.

GCF(16974,16982) = 2

We will now calculate the prime factors of 16974 and 16982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16974 and 16982.

How to find the GCF of 16974 and 16982?

We will first find the prime factorization of 16974 and 16982. After we will calculate the factors of 16974 and 16982 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 16982

Prime factors of 16982 are 2, 7, 1213. Prime factorization of 16982 in exponential form is:

16982 = 2¹ × 7¹ × 1213¹

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 16982

List of positive integer factors of 16982 that divides 16974 without a remainder.

1, 2, 7, 14, 1213, 2426, 8491

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16974 and 16982. The biggest common factor number is the GCF number.
So the greatest common factor 16974 and 16982 is 2.

Also check out the Least Common Multiple of 16974 and 16982