What is the Greatest Common Factor of 37674 and 37688?

Greatest common factor (GCF) of 37674 and 37688 is 14.

GCF(37674,37688) = 14

We will now calculate the prime factors of 37674 and 37688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37674 and 37688.

How to find the GCF of 37674 and 37688?

We will first find the prime factorization of 37674 and 37688. After we will calculate the factors of 37674 and 37688 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 37688

Prime factors of 37688 are 2, 7, 673. Prime factorization of 37688 in exponential form is:

37688 = 2³ × 7¹ × 673¹

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 37688

List of positive integer factors of 37688 that divides 37674 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 673, 1346, 2692, 4711, 5384, 9422, 18844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37674 and 37688. The biggest common factor number is the GCF number.
So the greatest common factor 37674 and 37688 is 14.

Also check out the Least Common Multiple of 37674 and 37688