What is the Greatest Common Factor of 37674 and 37690?

Greatest common factor (GCF) of 37674 and 37690 is 2.

GCF(37674,37690) = 2

We will now calculate the prime factors of 37674 and 37690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37674 and 37690.

How to find the GCF of 37674 and 37690?

We will first find the prime factorization of 37674 and 37690. After we will calculate the factors of 37674 and 37690 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 37690

Prime factors of 37690 are 2, 5, 3769. Prime factorization of 37690 in exponential form is:

37690 = 2¹ × 5¹ × 3769¹

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 37690

List of positive integer factors of 37690 that divides 37674 without a remainder.

1, 2, 5, 10, 3769, 7538, 18845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37674 and 37690. The biggest common factor number is the GCF number.
So the greatest common factor 37674 and 37690 is 2.

Also check out the Least Common Multiple of 37674 and 37690