What is the Greatest Common Factor of 37856 and 37874?

Greatest common factor (GCF) of 37856 and 37874 is 2.

GCF(37856,37874) = 2

We will now calculate the prime factors of 37856 and 37874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37856 and 37874.

How to find the GCF of 37856 and 37874?

We will first find the prime factorization of 37856 and 37874. After we will calculate the factors of 37856 and 37874 and find the biggest common factor number .

Step-1: Prime Factorization of 37856

Prime factors of 37856 are 2, 7, 13. Prime factorization of 37856 in exponential form is:

37856 = 2⁵ × 7¹ × 13²

Step-2: 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-3: Factors of 37856

List of positive integer factors of 37856 that divides 37856 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 169, 182, 208, 224, 338, 364, 416, 676, 728, 1183, 1352, 1456, 2366, 2704, 2912, 4732, 5408, 9464, 18928

Step-4: Factors of 37874

List of positive integer factors of 37874 that divides 37856 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37856 and 37874. The biggest common factor number is the GCF number.
So the greatest common factor 37856 and 37874 is 2.

Also check out the Least Common Multiple of 37856 and 37874