What is the Greatest Common Factor of 33670 and 33684?

Greatest common factor (GCF) of 33670 and 33684 is 14.

GCF(33670,33684) = 14

We will now calculate the prime factors of 33670 and 33684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33670 and 33684.

How to find the GCF of 33670 and 33684?

We will first find the prime factorization of 33670 and 33684. After we will calculate the factors of 33670 and 33684 and find the biggest common factor number .

Step-1: Prime Factorization of 33670

Prime factors of 33670 are 2, 5, 7, 13, 37. Prime factorization of 33670 in exponential form is:

33670 = 2¹ × 5¹ × 7¹ × 13¹ × 37¹

Step-2: Prime Factorization of 33684

Prime factors of 33684 are 2, 3, 7, 401. Prime factorization of 33684 in exponential form is:

33684 = 2² × 3¹ × 7¹ × 401¹

Step-3: Factors of 33670

List of positive integer factors of 33670 that divides 33670 without a remainder.

1, 2, 5, 7, 10, 13, 14, 26, 35, 37, 65, 70, 74, 91, 130, 182, 185, 259, 370, 455, 481, 518, 910, 962, 1295, 2405, 2590, 3367, 4810, 6734, 16835

Step-4: Factors of 33684

List of positive integer factors of 33684 that divides 33670 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 401, 802, 1203, 1604, 2406, 2807, 4812, 5614, 8421, 11228, 16842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33670 and 33684. The biggest common factor number is the GCF number.
So the greatest common factor 33670 and 33684 is 14.

Also check out the Least Common Multiple of 33670 and 33684