What is the Greatest Common Factor of 36750 and 36764?

Greatest common factor (GCF) of 36750 and 36764 is 14.

GCF(36750,36764) = 14

We will now calculate the prime factors of 36750 and 36764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36750 and 36764.

How to find the GCF of 36750 and 36764?

We will first find the prime factorization of 36750 and 36764. After we will calculate the factors of 36750 and 36764 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 36764

Prime factors of 36764 are 2, 7, 13, 101. Prime factorization of 36764 in exponential form is:

36764 = 2² × 7¹ × 13¹ × 101¹

Step-3: Factors of 36750

List of positive integer factors of 36750 that divides 36750 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

Step-4: Factors of 36764

List of positive integer factors of 36764 that divides 36750 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 101, 182, 202, 364, 404, 707, 1313, 1414, 2626, 2828, 5252, 9191, 18382

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36750 and 36764. The biggest common factor number is the GCF number.
So the greatest common factor 36750 and 36764 is 14.

Also check out the Least Common Multiple of 36750 and 36764