What is the Greatest Common Factor of 10225 and 10230?

Greatest common factor (GCF) of 10225 and 10230 is 5.

GCF(10225,10230) = 5

We will now calculate the prime factors of 10225 and 10230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10225 and 10230.

How to find the GCF of 10225 and 10230?

We will first find the prime factorization of 10225 and 10230. After we will calculate the factors of 10225 and 10230 and find the biggest common factor number .

Step-1: Prime Factorization of 10225

Prime factors of 10225 are 5, 409. Prime factorization of 10225 in exponential form is:

10225 = 5² × 409¹

Step-2: Prime Factorization of 10230

Prime factors of 10230 are 2, 3, 5, 11, 31. Prime factorization of 10230 in exponential form is:

10230 = 2¹ × 3¹ × 5¹ × 11¹ × 31¹

Step-3: Factors of 10225

List of positive integer factors of 10225 that divides 10225 without a remainder.

1, 5, 25, 409, 2045

Step-4: Factors of 10230

List of positive integer factors of 10230 that divides 10225 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 31, 33, 55, 62, 66, 93, 110, 155, 165, 186, 310, 330, 341, 465, 682, 930, 1023, 1705, 2046, 3410, 5115

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10225 and 10230. The biggest common factor number is the GCF number.
So the greatest common factor 10225 and 10230 is 5.

Also check out the Least Common Multiple of 10225 and 10230