What is the Greatest Common Factor of 37874 and 37888?

Greatest common factor (GCF) of 37874 and 37888 is 2.

GCF(37874,37888) = 2

We will now calculate the prime factors of 37874 and 37888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37874 and 37888.

How to find the GCF of 37874 and 37888?

We will first find the prime factorization of 37874 and 37888. After we will calculate the factors of 37874 and 37888 and find the biggest common factor number .

Step-1: Prime Factorization of 37874

Prime factors of 37874 are 2, 29, 653. Prime factorization of 37874 in exponential form is:

37874 = 2¹ × 29¹ × 653¹

Step-2: Prime Factorization of 37888

Prime factors of 37888 are 2, 37. Prime factorization of 37888 in exponential form is:

37888 = 2¹⁰ × 37¹

Step-3: Factors of 37874

List of positive integer factors of 37874 that divides 37874 without a remainder.

1, 2, 29, 58, 653, 1306, 18937

Step-4: Factors of 37888

List of positive integer factors of 37888 that divides 37874 without a remainder.

1, 2, 4, 8, 16, 32, 37, 64, 74, 128, 148, 256, 296, 512, 592, 1024, 1184, 2368, 4736, 9472, 18944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37874 and 37888. The biggest common factor number is the GCF number.
So the greatest common factor 37874 and 37888 is 2.

Also check out the Least Common Multiple of 37874 and 37888