What is the Greatest Common Factor of 10010 and 10023?

Greatest common factor (GCF) of 10010 and 10023 is 13.

GCF(10010,10023) = 13

We will now calculate the prime factors of 10010 and 10023, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10010 and 10023.

How to find the GCF of 10010 and 10023?

We will first find the prime factorization of 10010 and 10023. After we will calculate the factors of 10010 and 10023 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10023

Prime factors of 10023 are 3, 13, 257. Prime factorization of 10023 in exponential form is:

10023 = 3¹ × 13¹ × 257¹

Step-3: Factors of 10010

List of positive integer factors of 10010 that divides 10010 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

Step-4: Factors of 10023

List of positive integer factors of 10023 that divides 10010 without a remainder.

1, 3, 13, 39, 257, 771, 3341

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10010 and 10023. The biggest common factor number is the GCF number.
So the greatest common factor 10010 and 10023 is 13.

Also check out the Least Common Multiple of 10010 and 10023