What is the Greatest Common Factor of 10508 and 10514?

Greatest common factor (GCF) of 10508 and 10514 is 2.

GCF(10508,10514) = 2

We will now calculate the prime factors of 10508 and 10514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10508 and 10514.

How to find the GCF of 10508 and 10514?

We will first find the prime factorization of 10508 and 10514. After we will calculate the factors of 10508 and 10514 and find the biggest common factor number .

Step-1: Prime Factorization of 10508

Prime factors of 10508 are 2, 37, 71. Prime factorization of 10508 in exponential form is:

10508 = 2² × 37¹ × 71¹

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 10508

List of positive integer factors of 10508 that divides 10508 without a remainder.

1, 2, 4, 37, 71, 74, 142, 148, 284, 2627, 5254

Step-4: Factors of 10514

List of positive integer factors of 10514 that divides 10508 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10508 and 10514. The biggest common factor number is the GCF number.
So the greatest common factor 10508 and 10514 is 2.

Also check out the Least Common Multiple of 10508 and 10514