What is the Greatest Common Factor of 16974 and 16984?

Greatest common factor (GCF) of 16974 and 16984 is 2.

GCF(16974,16984) = 2

We will now calculate the prime factors of 16974 and 16984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16974 and 16984.

How to find the GCF of 16974 and 16984?

We will first find the prime factorization of 16974 and 16984. After we will calculate the factors of 16974 and 16984 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 16984

Prime factors of 16984 are 2, 11, 193. Prime factorization of 16984 in exponential form is:

16984 = 2³ × 11¹ × 193¹

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 16984

List of positive integer factors of 16984 that divides 16974 without a remainder.

1, 2, 4, 8, 11, 22, 44, 88, 193, 386, 772, 1544, 2123, 4246, 8492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16974 and 16984. The biggest common factor number is the GCF number.
So the greatest common factor 16974 and 16984 is 2.

Also check out the Least Common Multiple of 16974 and 16984