What is the Greatest Common Factor of 37408 and 37422?

Greatest common factor (GCF) of 37408 and 37422 is 14.

GCF(37408,37422) = 14

We will now calculate the prime factors of 37408 and 37422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37408 and 37422.

How to find the GCF of 37408 and 37422?

We will first find the prime factorization of 37408 and 37422. After we will calculate the factors of 37408 and 37422 and find the biggest common factor number .

Step-1: Prime Factorization of 37408

Prime factors of 37408 are 2, 7, 167. Prime factorization of 37408 in exponential form is:

37408 = 2⁵ × 7¹ × 167¹

Step-2: Prime Factorization of 37422

Prime factors of 37422 are 2, 3, 7, 11. Prime factorization of 37422 in exponential form is:

37422 = 2¹ × 3⁵ × 7¹ × 11¹

Step-3: Factors of 37408

List of positive integer factors of 37408 that divides 37408 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 167, 224, 334, 668, 1169, 1336, 2338, 2672, 4676, 5344, 9352, 18704

Step-4: Factors of 37422

List of positive integer factors of 37422 that divides 37408 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 27, 33, 42, 54, 63, 66, 77, 81, 99, 126, 154, 162, 189, 198, 231, 243, 297, 378, 462, 486, 567, 594, 693, 891, 1134, 1386, 1701, 1782, 2079, 2673, 3402, 4158, 5346, 6237, 12474, 18711

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37408 and 37422. The biggest common factor number is the GCF number.
So the greatest common factor 37408 and 37422 is 14.

Also check out the Least Common Multiple of 37408 and 37422