What is the Greatest Common Factor of 10005 and 10010?

Greatest common factor (GCF) of 10005 and 10010 is 5.

GCF(10005,10010) = 5

We will now calculate the prime factors of 10005 and 10010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10005 and 10010.

How to find the GCF of 10005 and 10010?

We will first find the prime factorization of 10005 and 10010. After we will calculate the factors of 10005 and 10010 and find the biggest common factor number .

Step-1: Prime Factorization of 10005

Prime factors of 10005 are 3, 5, 23, 29. Prime factorization of 10005 in exponential form is:

10005 = 3¹ × 5¹ × 23¹ × 29¹

Step-2: Prime Factorization of 10010

Prime factors of 10010 are 2, 5, 7, 11, 13. Prime factorization of 10010 in exponential form is:

10010 = 2¹ × 5¹ × 7¹ × 11¹ × 13¹

Step-3: Factors of 10005

List of positive integer factors of 10005 that divides 10005 without a remainder.

1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335

Step-4: Factors of 10010

List of positive integer factors of 10010 that divides 10005 without a remainder.

1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10005 and 10010. The biggest common factor number is the GCF number.
So the greatest common factor 10005 and 10010 is 5.

Also check out the Least Common Multiple of 10005 and 10010