What is the Greatest Common Factor of 37380 and 37394?

Greatest common factor (GCF) of 37380 and 37394 is 14.

GCF(37380,37394) = 14

We will now calculate the prime factors of 37380 and 37394, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37380 and 37394.

How to find the GCF of 37380 and 37394?

We will first find the prime factorization of 37380 and 37394. After we will calculate the factors of 37380 and 37394 and find the biggest common factor number .

Step-1: Prime Factorization of 37380

Prime factors of 37380 are 2, 3, 5, 7, 89. Prime factorization of 37380 in exponential form is:

37380 = 2² × 3¹ × 5¹ × 7¹ × 89¹

Step-2: Prime Factorization of 37394

Prime factors of 37394 are 2, 7, 2671. Prime factorization of 37394 in exponential form is:

37394 = 2¹ × 7¹ × 2671¹

Step-3: Factors of 37380

List of positive integer factors of 37380 that divides 37380 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 89, 105, 140, 178, 210, 267, 356, 420, 445, 534, 623, 890, 1068, 1246, 1335, 1780, 1869, 2492, 2670, 3115, 3738, 5340, 6230, 7476, 9345, 12460, 18690

Step-4: Factors of 37394

List of positive integer factors of 37394 that divides 37380 without a remainder.

1, 2, 7, 14, 2671, 5342, 18697

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37380 and 37394. The biggest common factor number is the GCF number.
So the greatest common factor 37380 and 37394 is 14.

Also check out the Least Common Multiple of 37380 and 37394