What is the Greatest Common Factor of 10600 and 10614?

Greatest common factor (GCF) of 10600 and 10614 is 2.

GCF(10600,10614) = 2

We will now calculate the prime factors of 10600 and 10614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10600 and 10614.

How to find the GCF of 10600 and 10614?

We will first find the prime factorization of 10600 and 10614. After we will calculate the factors of 10600 and 10614 and find the biggest common factor number .

Step-1: Prime Factorization of 10600

Prime factors of 10600 are 2, 5, 53. Prime factorization of 10600 in exponential form is:

10600 = 2³ × 5² × 53¹

Step-2: Prime Factorization of 10614

Prime factors of 10614 are 2, 3, 29, 61. Prime factorization of 10614 in exponential form is:

10614 = 2¹ × 3¹ × 29¹ × 61¹

Step-3: Factors of 10600

List of positive integer factors of 10600 that divides 10600 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 53, 100, 106, 200, 212, 265, 424, 530, 1060, 1325, 2120, 2650, 5300

Step-4: Factors of 10614

List of positive integer factors of 10614 that divides 10600 without a remainder.

1, 2, 3, 6, 29, 58, 61, 87, 122, 174, 183, 366, 1769, 3538, 5307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10600 and 10614. The biggest common factor number is the GCF number.
So the greatest common factor 10600 and 10614 is 2.

Also check out the Least Common Multiple of 10600 and 10614