What is the Greatest Common Factor of 36984 and 37000?

Greatest common factor (GCF) of 36984 and 37000 is 8.

GCF(36984,37000) = 8

We will now calculate the prime factors of 36984 and 37000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36984 and 37000.

How to find the GCF of 36984 and 37000?

We will first find the prime factorization of 36984 and 37000. After we will calculate the factors of 36984 and 37000 and find the biggest common factor number .

Step-1: Prime Factorization of 36984

Prime factors of 36984 are 2, 3, 23, 67. Prime factorization of 36984 in exponential form is:

36984 = 2³ × 3¹ × 23¹ × 67¹

Step-2: Prime Factorization of 37000

Prime factors of 37000 are 2, 5, 37. Prime factorization of 37000 in exponential form is:

37000 = 2³ × 5³ × 37¹

Step-3: Factors of 36984

List of positive integer factors of 36984 that divides 36984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 67, 69, 92, 134, 138, 184, 201, 268, 276, 402, 536, 552, 804, 1541, 1608, 3082, 4623, 6164, 9246, 12328, 18492

Step-4: Factors of 37000

List of positive integer factors of 37000 that divides 36984 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 37, 40, 50, 74, 100, 125, 148, 185, 200, 250, 296, 370, 500, 740, 925, 1000, 1480, 1850, 3700, 4625, 7400, 9250, 18500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36984 and 37000. The biggest common factor number is the GCF number.
So the greatest common factor 36984 and 37000 is 8.

Also check out the Least Common Multiple of 36984 and 37000