What is the Greatest Common Factor of 33750 and 33768?

Greatest common factor (GCF) of 33750 and 33768 is 18.

GCF(33750,33768) = 18

We will now calculate the prime factors of 33750 and 33768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33750 and 33768.

How to find the GCF of 33750 and 33768?

We will first find the prime factorization of 33750 and 33768. After we will calculate the factors of 33750 and 33768 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 33768

Prime factors of 33768 are 2, 3, 7, 67. Prime factorization of 33768 in exponential form is:

33768 = 2³ × 3² × 7¹ × 67¹

Step-3: Factors of 33750

List of positive integer factors of 33750 that divides 33750 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

Step-4: Factors of 33768

List of positive integer factors of 33768 that divides 33750 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 67, 72, 84, 126, 134, 168, 201, 252, 268, 402, 469, 504, 536, 603, 804, 938, 1206, 1407, 1608, 1876, 2412, 2814, 3752, 4221, 4824, 5628, 8442, 11256, 16884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33750 and 33768. The biggest common factor number is the GCF number.
So the greatest common factor 33750 and 33768 is 18.

Also check out the Least Common Multiple of 33750 and 33768