What is the Greatest Common Factor of 33735 and 33750?

Greatest common factor (GCF) of 33735 and 33750 is 15.

GCF(33735,33750) = 15

We will now calculate the prime factors of 33735 and 33750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33735 and 33750.

How to find the GCF of 33735 and 33750?

We will first find the prime factorization of 33735 and 33750. After we will calculate the factors of 33735 and 33750 and find the biggest common factor number .

Step-1: Prime Factorization of 33735

Prime factors of 33735 are 3, 5, 13, 173. Prime factorization of 33735 in exponential form is:

33735 = 3¹ × 5¹ × 13¹ × 173¹

Step-2: Prime Factorization of 33750

Prime factors of 33750 are 2, 3, 5. Prime factorization of 33750 in exponential form is:

33750 = 2¹ × 3³ × 5⁴

Step-3: Factors of 33735

List of positive integer factors of 33735 that divides 33735 without a remainder.

1, 3, 5, 13, 15, 39, 65, 173, 195, 519, 865, 2249, 2595, 6747, 11245

Step-4: Factors of 33750

List of positive integer factors of 33750 that divides 33735 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 125, 135, 150, 225, 250, 270, 375, 450, 625, 675, 750, 1125, 1250, 1350, 1875, 2250, 3375, 3750, 5625, 6750, 11250, 16875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33735 and 33750. The biggest common factor number is the GCF number.
So the greatest common factor 33735 and 33750 is 15.

Also check out the Least Common Multiple of 33735 and 33750