What is the Greatest Common Factor of 37744 and 37758?

Greatest common factor (GCF) of 37744 and 37758 is 14.

GCF(37744,37758) = 14

We will now calculate the prime factors of 37744 and 37758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37744 and 37758.

How to find the GCF of 37744 and 37758?

We will first find the prime factorization of 37744 and 37758. After we will calculate the factors of 37744 and 37758 and find the biggest common factor number .

Step-1: Prime Factorization of 37744

Prime factors of 37744 are 2, 7, 337. Prime factorization of 37744 in exponential form is:

37744 = 2⁴ × 7¹ × 337¹

Step-2: Prime Factorization of 37758

Prime factors of 37758 are 2, 3, 7, 29, 31. Prime factorization of 37758 in exponential form is:

37758 = 2¹ × 3¹ × 7¹ × 29¹ × 31¹

Step-3: Factors of 37744

List of positive integer factors of 37744 that divides 37744 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 337, 674, 1348, 2359, 2696, 4718, 5392, 9436, 18872

Step-4: Factors of 37758

List of positive integer factors of 37758 that divides 37744 without a remainder.

1, 2, 3, 6, 7, 14, 21, 29, 31, 42, 58, 62, 87, 93, 174, 186, 203, 217, 406, 434, 609, 651, 899, 1218, 1302, 1798, 2697, 5394, 6293, 12586, 18879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37744 and 37758. The biggest common factor number is the GCF number.
So the greatest common factor 37744 and 37758 is 14.

Also check out the Least Common Multiple of 37744 and 37758