What is the Greatest Common Factor of 33500 and 33514?

Greatest common factor (GCF) of 33500 and 33514 is 2.

GCF(33500,33514) = 2

We will now calculate the prime factors of 33500 and 33514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33500 and 33514.

How to find the GCF of 33500 and 33514?

We will first find the prime factorization of 33500 and 33514. After we will calculate the factors of 33500 and 33514 and find the biggest common factor number .

Step-1: Prime Factorization of 33500

Prime factors of 33500 are 2, 5, 67. Prime factorization of 33500 in exponential form is:

33500 = 2² × 5³ × 67¹

Step-2: Prime Factorization of 33514

Prime factors of 33514 are 2, 13, 1289. Prime factorization of 33514 in exponential form is:

33514 = 2¹ × 13¹ × 1289¹

Step-3: Factors of 33500

List of positive integer factors of 33500 that divides 33500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 67, 100, 125, 134, 250, 268, 335, 500, 670, 1340, 1675, 3350, 6700, 8375, 16750

Step-4: Factors of 33514

List of positive integer factors of 33514 that divides 33500 without a remainder.

1, 2, 13, 26, 1289, 2578, 16757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33500 and 33514. The biggest common factor number is the GCF number.
So the greatest common factor 33500 and 33514 is 2.

Also check out the Least Common Multiple of 33500 and 33514