What is the Greatest Common Factor of 37674 and 37683?

Greatest common factor (GCF) of 37674 and 37683 is 9.

GCF(37674,37683) = 9

We will now calculate the prime factors of 37674 and 37683, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37674 and 37683.

How to find the GCF of 37674 and 37683?

We will first find the prime factorization of 37674 and 37683. After we will calculate the factors of 37674 and 37683 and find the biggest common factor number .

Step-1: Prime Factorization of 37674

Prime factors of 37674 are 2, 3, 7, 13, 23. Prime factorization of 37674 in exponential form is:

37674 = 2¹ × 3² × 7¹ × 13¹ × 23¹

Step-2: Prime Factorization of 37683

Prime factors of 37683 are 3, 53, 79. Prime factorization of 37683 in exponential form is:

37683 = 3² × 53¹ × 79¹

Step-3: Factors of 37674

List of positive integer factors of 37674 that divides 37674 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 23, 26, 39, 42, 46, 63, 69, 78, 91, 117, 126, 138, 161, 182, 207, 234, 273, 299, 322, 414, 483, 546, 598, 819, 897, 966, 1449, 1638, 1794, 2093, 2691, 2898, 4186, 5382, 6279, 12558, 18837

Step-4: Factors of 37683

List of positive integer factors of 37683 that divides 37674 without a remainder.

1, 3, 9, 53, 79, 159, 237, 477, 711, 4187, 12561

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37674 and 37683. The biggest common factor number is the GCF number.
So the greatest common factor 37674 and 37683 is 9.

Also check out the Least Common Multiple of 37674 and 37683