What is the Greatest Common Factor of 36735 and 36750?

Greatest common factor (GCF) of 36735 and 36750 is 15.

GCF(36735,36750) = 15

We will now calculate the prime factors of 36735 and 36750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36735 and 36750.

How to find the GCF of 36735 and 36750?

We will first find the prime factorization of 36735 and 36750. After we will calculate the factors of 36735 and 36750 and find the biggest common factor number .

Step-1: Prime Factorization of 36735

Prime factors of 36735 are 3, 5, 31, 79. Prime factorization of 36735 in exponential form is:

36735 = 3¹ × 5¹ × 31¹ × 79¹

Step-2: Prime Factorization of 36750

Prime factors of 36750 are 2, 3, 5, 7. Prime factorization of 36750 in exponential form is:

36750 = 2¹ × 3¹ × 5³ × 7²

Step-3: Factors of 36735

List of positive integer factors of 36735 that divides 36735 without a remainder.

1, 3, 5, 15, 31, 79, 93, 155, 237, 395, 465, 1185, 2449, 7347, 12245

Step-4: Factors of 36750

List of positive integer factors of 36750 that divides 36735 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 49, 50, 70, 75, 98, 105, 125, 147, 150, 175, 210, 245, 250, 294, 350, 375, 490, 525, 735, 750, 875, 1050, 1225, 1470, 1750, 2450, 2625, 3675, 5250, 6125, 7350, 12250, 18375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36735 and 36750. The biggest common factor number is the GCF number.
So the greatest common factor 36735 and 36750 is 15.

Also check out the Least Common Multiple of 36735 and 36750