What is the Greatest Common Factor of 37658 and 37674?

Greatest common factor (GCF) of 37658 and 37674 is 2.

GCF(37658,37674) = 2

We will now calculate the prime factors of 37658 and 37674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37658 and 37674.

How to find the GCF of 37658 and 37674?

We will first find the prime factorization of 37658 and 37674. After we will calculate the factors of 37658 and 37674 and find the biggest common factor number .

Step-1: Prime Factorization of 37658

Prime factors of 37658 are 2, 19, 991. Prime factorization of 37658 in exponential form is:

37658 = 2¹ × 19¹ × 991¹

Step-2: 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-3: Factors of 37658

List of positive integer factors of 37658 that divides 37658 without a remainder.

1, 2, 19, 38, 991, 1982, 18829

Step-4: Factors of 37674

List of positive integer factors of 37674 that divides 37658 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37658 and 37674. The biggest common factor number is the GCF number.
So the greatest common factor 37658 and 37674 is 2.

Also check out the Least Common Multiple of 37658 and 37674