What is the Greatest Common Factor of 37734 and 37742?

Greatest common factor (GCF) of 37734 and 37742 is 2.

GCF(37734,37742) = 2

We will now calculate the prime factors of 37734 and 37742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37734 and 37742.

How to find the GCF of 37734 and 37742?

We will first find the prime factorization of 37734 and 37742. After we will calculate the factors of 37734 and 37742 and find the biggest common factor number .

Step-1: Prime Factorization of 37734

Prime factors of 37734 are 2, 3, 19, 331. Prime factorization of 37734 in exponential form is:

37734 = 2¹ × 3¹ × 19¹ × 331¹

Step-2: Prime Factorization of 37742

Prime factors of 37742 are 2, 113, 167. Prime factorization of 37742 in exponential form is:

37742 = 2¹ × 113¹ × 167¹

Step-3: Factors of 37734

List of positive integer factors of 37734 that divides 37734 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 331, 662, 993, 1986, 6289, 12578, 18867

Step-4: Factors of 37742

List of positive integer factors of 37742 that divides 37734 without a remainder.

1, 2, 113, 167, 226, 334, 18871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37734 and 37742. The biggest common factor number is the GCF number.
So the greatest common factor 37734 and 37742 is 2.

Also check out the Least Common Multiple of 37734 and 37742