What is the Greatest Common Factor of 37674 and 37682?

Greatest common factor (GCF) of 37674 and 37682 is 2.

GCF(37674,37682) = 2

We will now calculate the prime factors of 37674 and 37682, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37674 and 37682.

How to find the GCF of 37674 and 37682?

We will first find the prime factorization of 37674 and 37682. After we will calculate the factors of 37674 and 37682 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 37682

Prime factors of 37682 are 2, 83, 227. Prime factorization of 37682 in exponential form is:

37682 = 2¹ × 83¹ × 227¹

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 37682

List of positive integer factors of 37682 that divides 37674 without a remainder.

1, 2, 83, 166, 227, 454, 18841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37674 and 37682. The biggest common factor number is the GCF number.
So the greatest common factor 37674 and 37682 is 2.

Also check out the Least Common Multiple of 37674 and 37682