What is the Greatest Common Factor of 10496 and 10514?

Greatest common factor (GCF) of 10496 and 10514 is 2.

GCF(10496,10514) = 2

We will now calculate the prime factors of 10496 and 10514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10496 and 10514.

How to find the GCF of 10496 and 10514?

We will first find the prime factorization of 10496 and 10514. After we will calculate the factors of 10496 and 10514 and find the biggest common factor number .

Step-1: Prime Factorization of 10496

Prime factors of 10496 are 2, 41. Prime factorization of 10496 in exponential form is:

10496 = 2⁸ × 41¹

Step-2: Prime Factorization of 10514

Prime factors of 10514 are 2, 7, 751. Prime factorization of 10514 in exponential form is:

10514 = 2¹ × 7¹ × 751¹

Step-3: Factors of 10496

List of positive integer factors of 10496 that divides 10496 without a remainder.

1, 2, 4, 8, 16, 32, 41, 64, 82, 128, 164, 256, 328, 656, 1312, 2624, 5248

Step-4: Factors of 10514

List of positive integer factors of 10514 that divides 10496 without a remainder.

1, 2, 7, 14, 751, 1502, 5257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10496 and 10514. The biggest common factor number is the GCF number.
So the greatest common factor 10496 and 10514 is 2.

Also check out the Least Common Multiple of 10496 and 10514