What is the Greatest Common Factor of 37294 and 37312?

Greatest common factor (GCF) of 37294 and 37312 is 2.

GCF(37294,37312) = 2

We will now calculate the prime factors of 37294 and 37312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37294 and 37312.

How to find the GCF of 37294 and 37312?

We will first find the prime factorization of 37294 and 37312. After we will calculate the factors of 37294 and 37312 and find the biggest common factor number .

Step-1: Prime Factorization of 37294

Prime factors of 37294 are 2, 29, 643. Prime factorization of 37294 in exponential form is:

37294 = 2¹ × 29¹ × 643¹

Step-2: Prime Factorization of 37312

Prime factors of 37312 are 2, 11, 53. Prime factorization of 37312 in exponential form is:

37312 = 2⁶ × 11¹ × 53¹

Step-3: Factors of 37294

List of positive integer factors of 37294 that divides 37294 without a remainder.

1, 2, 29, 58, 643, 1286, 18647

Step-4: Factors of 37312

List of positive integer factors of 37312 that divides 37294 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 53, 64, 88, 106, 176, 212, 352, 424, 583, 704, 848, 1166, 1696, 2332, 3392, 4664, 9328, 18656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37294 and 37312. The biggest common factor number is the GCF number.
So the greatest common factor 37294 and 37312 is 2.

Also check out the Least Common Multiple of 37294 and 37312