What is the Greatest Common Factor of 10725 and 10740?

Greatest common factor (GCF) of 10725 and 10740 is 15.

GCF(10725,10740) = 15

We will now calculate the prime factors of 10725 and 10740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10725 and 10740.

How to find the GCF of 10725 and 10740?

We will first find the prime factorization of 10725 and 10740. After we will calculate the factors of 10725 and 10740 and find the biggest common factor number .

Step-1: Prime Factorization of 10725

Prime factors of 10725 are 3, 5, 11, 13. Prime factorization of 10725 in exponential form is:

10725 = 3¹ × 5² × 11¹ × 13¹

Step-2: Prime Factorization of 10740

Prime factors of 10740 are 2, 3, 5, 179. Prime factorization of 10740 in exponential form is:

10740 = 2² × 3¹ × 5¹ × 179¹

Step-3: Factors of 10725

List of positive integer factors of 10725 that divides 10725 without a remainder.

1, 3, 5, 11, 13, 15, 25, 33, 39, 55, 65, 75, 143, 165, 195, 275, 325, 429, 715, 825, 975, 2145, 3575

Step-4: Factors of 10740

List of positive integer factors of 10740 that divides 10725 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 179, 358, 537, 716, 895, 1074, 1790, 2148, 2685, 3580, 5370

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10725 and 10740. The biggest common factor number is the GCF number.
So the greatest common factor 10725 and 10740 is 15.

Also check out the Least Common Multiple of 10725 and 10740