What is the Greatest Common Factor of 10234 and 10251?

Greatest common factor (GCF) of 10234 and 10251 is 17.

GCF(10234,10251) = 17

We will now calculate the prime factors of 10234 and 10251, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10234 and 10251.

How to find the GCF of 10234 and 10251?

We will first find the prime factorization of 10234 and 10251. After we will calculate the factors of 10234 and 10251 and find the biggest common factor number .

Step-1: Prime Factorization of 10234

Prime factors of 10234 are 2, 7, 17, 43. Prime factorization of 10234 in exponential form is:

10234 = 2¹ × 7¹ × 17¹ × 43¹

Step-2: Prime Factorization of 10251

Prime factors of 10251 are 3, 17, 67. Prime factorization of 10251 in exponential form is:

10251 = 3² × 17¹ × 67¹

Step-3: Factors of 10234

List of positive integer factors of 10234 that divides 10234 without a remainder.

1, 2, 7, 14, 17, 34, 43, 86, 119, 238, 301, 602, 731, 1462, 5117

Step-4: Factors of 10251

List of positive integer factors of 10251 that divides 10234 without a remainder.

1, 3, 9, 17, 51, 67, 153, 201, 603, 1139, 3417

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10234 and 10251. The biggest common factor number is the GCF number.
So the greatest common factor 10234 and 10251 is 17.

Also check out the Least Common Multiple of 10234 and 10251