What is the Greatest Common Factor of 16500 and 16514?

Greatest common factor (GCF) of 16500 and 16514 is 2.

GCF(16500,16514) = 2

We will now calculate the prime factors of 16500 and 16514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16500 and 16514.

How to find the GCF of 16500 and 16514?

We will first find the prime factorization of 16500 and 16514. After we will calculate the factors of 16500 and 16514 and find the biggest common factor number .

Step-1: Prime Factorization of 16500

Prime factors of 16500 are 2, 3, 5, 11. Prime factorization of 16500 in exponential form is:

16500 = 2² × 3¹ × 5³ × 11¹

Step-2: Prime Factorization of 16514

Prime factors of 16514 are 2, 23, 359. Prime factorization of 16514 in exponential form is:

16514 = 2¹ × 23¹ × 359¹

Step-3: Factors of 16500

List of positive integer factors of 16500 that divides 16500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 125, 132, 150, 165, 220, 250, 275, 300, 330, 375, 500, 550, 660, 750, 825, 1100, 1375, 1500, 1650, 2750, 3300, 4125, 5500, 8250

Step-4: Factors of 16514

List of positive integer factors of 16514 that divides 16500 without a remainder.

1, 2, 23, 46, 359, 718, 8257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16500 and 16514. The biggest common factor number is the GCF number.
So the greatest common factor 16500 and 16514 is 2.

Also check out the Least Common Multiple of 16500 and 16514