What is the Greatest Common Factor of 37660 and 37674?

Greatest common factor (GCF) of 37660 and 37674 is 14.

GCF(37660,37674) = 14

We will now calculate the prime factors of 37660 and 37674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37660 and 37674.

How to find the GCF of 37660 and 37674?

We will first find the prime factorization of 37660 and 37674. After we will calculate the factors of 37660 and 37674 and find the biggest common factor number .

Step-1: Prime Factorization of 37660

Prime factors of 37660 are 2, 5, 7, 269. Prime factorization of 37660 in exponential form is:

37660 = 2² × 5¹ × 7¹ × 269¹

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 37660

List of positive integer factors of 37660 that divides 37660 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 269, 538, 1076, 1345, 1883, 2690, 3766, 5380, 7532, 9415, 18830

Step-4: Factors of 37674

List of positive integer factors of 37674 that divides 37660 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 37660 and 37674. The biggest common factor number is the GCF number.
So the greatest common factor 37660 and 37674 is 14.

Also check out the Least Common Multiple of 37660 and 37674