What is the Greatest Common Factor of 10258 and 10272?

Greatest common factor (GCF) of 10258 and 10272 is 2.

GCF(10258,10272) = 2

We will now calculate the prime factors of 10258 and 10272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10258 and 10272.

How to find the GCF of 10258 and 10272?

We will first find the prime factorization of 10258 and 10272. After we will calculate the factors of 10258 and 10272 and find the biggest common factor number .

Step-1: Prime Factorization of 10258

Prime factors of 10258 are 2, 23, 223. Prime factorization of 10258 in exponential form is:

10258 = 2¹ × 23¹ × 223¹

Step-2: Prime Factorization of 10272

Prime factors of 10272 are 2, 3, 107. Prime factorization of 10272 in exponential form is:

10272 = 2⁵ × 3¹ × 107¹

Step-3: Factors of 10258

List of positive integer factors of 10258 that divides 10258 without a remainder.

1, 2, 23, 46, 223, 446, 5129

Step-4: Factors of 10272

List of positive integer factors of 10272 that divides 10258 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 107, 214, 321, 428, 642, 856, 1284, 1712, 2568, 3424, 5136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10258 and 10272. The biggest common factor number is the GCF number.
So the greatest common factor 10258 and 10272 is 2.

Also check out the Least Common Multiple of 10258 and 10272