What is the Greatest Common Factor of 33628 and 33642?

Greatest common factor (GCF) of 33628 and 33642 is 14.

GCF(33628,33642) = 14

We will now calculate the prime factors of 33628 and 33642, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33628 and 33642.

How to find the GCF of 33628 and 33642?

We will first find the prime factorization of 33628 and 33642. After we will calculate the factors of 33628 and 33642 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 33642

Prime factors of 33642 are 2, 3, 7, 89. Prime factorization of 33642 in exponential form is:

33642 = 2¹ × 3³ × 7¹ × 89¹

Step-3: Factors of 33628

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

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

Step-4: Factors of 33642

List of positive integer factors of 33642 that divides 33628 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 89, 126, 178, 189, 267, 378, 534, 623, 801, 1246, 1602, 1869, 2403, 3738, 4806, 5607, 11214, 16821

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33628 and 33642. The biggest common factor number is the GCF number.
So the greatest common factor 33628 and 33642 is 14.

Also check out the Least Common Multiple of 33628 and 33642