What is the Greatest Common Factor of 33614 and 33628?

Greatest common factor (GCF) of 33614 and 33628 is 14.

GCF(33614,33628) = 14

We will now calculate the prime factors of 33614 and 33628, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33614 and 33628.

How to find the GCF of 33614 and 33628?

We will first find the prime factorization of 33614 and 33628. After we will calculate the factors of 33614 and 33628 and find the biggest common factor number .

Step-1: Prime Factorization of 33614

Prime factors of 33614 are 2, 7. Prime factorization of 33614 in exponential form is:

33614 = 2¹ × 7⁵

Step-2: Prime Factorization of 33628

Prime factors of 33628 are 2, 7, 1201. Prime factorization of 33628 in exponential form is:

33628 = 2² × 7¹ × 1201¹

Step-3: Factors of 33614

List of positive integer factors of 33614 that divides 33614 without a remainder.

1, 2, 7, 14, 49, 98, 343, 686, 2401, 4802, 16807

Step-4: Factors of 33628

List of positive integer factors of 33628 that divides 33614 without a remainder.

1, 2, 4, 7, 14, 28, 1201, 2402, 4804, 8407, 16814

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33614 and 33628. The biggest common factor number is the GCF number.
So the greatest common factor 33614 and 33628 is 14.

Also check out the Least Common Multiple of 33614 and 33628