What is the Greatest Common Factor of 10725 and 10730?

Greatest common factor (GCF) of 10725 and 10730 is 5.

GCF(10725,10730) = 5

We will now calculate the prime factors of 10725 and 10730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10725 and 10730.

How to find the GCF of 10725 and 10730?

We will first find the prime factorization of 10725 and 10730. After we will calculate the factors of 10725 and 10730 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 10730

Prime factors of 10730 are 2, 5, 29, 37. Prime factorization of 10730 in exponential form is:

10730 = 2¹ × 5¹ × 29¹ × 37¹

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 10730

List of positive integer factors of 10730 that divides 10725 without a remainder.

1, 2, 5, 10, 29, 37, 58, 74, 145, 185, 290, 370, 1073, 2146, 5365

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10725 and 10730. The biggest common factor number is the GCF number.
So the greatest common factor 10725 and 10730 is 5.

Also check out the Least Common Multiple of 10725 and 10730