What is the Greatest Common Factor of 37400 and 37408?

Greatest common factor (GCF) of 37400 and 37408 is 8.

GCF(37400,37408) = 8

We will now calculate the prime factors of 37400 and 37408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37400 and 37408.

How to find the GCF of 37400 and 37408?

We will first find the prime factorization of 37400 and 37408. After we will calculate the factors of 37400 and 37408 and find the biggest common factor number .

Step-1: Prime Factorization of 37400

Prime factors of 37400 are 2, 5, 11, 17. Prime factorization of 37400 in exponential form is:

37400 = 2³ × 5² × 11¹ × 17¹

Step-2: 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-3: Factors of 37400

List of positive integer factors of 37400 that divides 37400 without a remainder.

1, 2, 4, 5, 8, 10, 11, 17, 20, 22, 25, 34, 40, 44, 50, 55, 68, 85, 88, 100, 110, 136, 170, 187, 200, 220, 275, 340, 374, 425, 440, 550, 680, 748, 850, 935, 1100, 1496, 1700, 1870, 2200, 3400, 3740, 4675, 7480, 9350, 18700

Step-4: Factors of 37408

List of positive integer factors of 37408 that divides 37400 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37400 and 37408. The biggest common factor number is the GCF number.
So the greatest common factor 37400 and 37408 is 8.

Also check out the Least Common Multiple of 37400 and 37408