What is the Greatest Common Factor of 37188 and 37200?

Greatest common factor (GCF) of 37188 and 37200 is 12.

GCF(37188,37200) = 12

We will now calculate the prime factors of 37188 and 37200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37188 and 37200.

How to find the GCF of 37188 and 37200?

We will first find the prime factorization of 37188 and 37200. After we will calculate the factors of 37188 and 37200 and find the biggest common factor number .

Step-1: Prime Factorization of 37188

Prime factors of 37188 are 2, 3, 1033. Prime factorization of 37188 in exponential form is:

37188 = 2² × 3² × 1033¹

Step-2: Prime Factorization of 37200

Prime factors of 37200 are 2, 3, 5, 31. Prime factorization of 37200 in exponential form is:

37200 = 2⁴ × 3¹ × 5² × 31¹

Step-3: Factors of 37188

List of positive integer factors of 37188 that divides 37188 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1033, 2066, 3099, 4132, 6198, 9297, 12396, 18594

Step-4: Factors of 37200

List of positive integer factors of 37200 that divides 37188 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 31, 40, 48, 50, 60, 62, 75, 80, 93, 100, 120, 124, 150, 155, 186, 200, 240, 248, 300, 310, 372, 400, 465, 496, 600, 620, 744, 775, 930, 1200, 1240, 1488, 1550, 1860, 2325, 2480, 3100, 3720, 4650, 6200, 7440, 9300, 12400, 18600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37188 and 37200. The biggest common factor number is the GCF number.
So the greatest common factor 37188 and 37200 is 12.

Also check out the Least Common Multiple of 37188 and 37200