What is the Greatest Common Factor of 37874 and 37884?

Greatest common factor (GCF) of 37874 and 37884 is 2.

GCF(37874,37884) = 2

We will now calculate the prime factors of 37874 and 37884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37874 and 37884.

How to find the GCF of 37874 and 37884?

We will first find the prime factorization of 37874 and 37884. After we will calculate the factors of 37874 and 37884 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 37884

Prime factors of 37884 are 2, 3, 7, 11, 41. Prime factorization of 37884 in exponential form is:

37884 = 2² × 3¹ × 7¹ × 11¹ × 41¹

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 37884

List of positive integer factors of 37884 that divides 37874 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 41, 42, 44, 66, 77, 82, 84, 123, 132, 154, 164, 231, 246, 287, 308, 451, 462, 492, 574, 861, 902, 924, 1148, 1353, 1722, 1804, 2706, 3157, 3444, 5412, 6314, 9471, 12628, 18942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37874 and 37884. The biggest common factor number is the GCF number.
So the greatest common factor 37874 and 37884 is 2.

Also check out the Least Common Multiple of 37874 and 37884