What is the Greatest Common Factor of 33689 and 33705?

Greatest common factor (GCF) of 33689 and 33705 is 1.

GCF(33689,33705) = 1

We will now calculate the prime factors of 33689 and 33705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33689 and 33705.

How to find the GCF of 33689 and 33705?

We will first find the prime factorization of 33689 and 33705. After we will calculate the factors of 33689 and 33705 and find the biggest common factor number .

Step-1: Prime Factorization of 33689

Prime factors of 33689 are 59, 571. Prime factorization of 33689 in exponential form is:

33689 = 59¹ × 571¹

Step-2: Prime Factorization of 33705

Prime factors of 33705 are 3, 5, 7, 107. Prime factorization of 33705 in exponential form is:

33705 = 3² × 5¹ × 7¹ × 107¹

Step-3: Factors of 33689

List of positive integer factors of 33689 that divides 33689 without a remainder.

1, 59, 571

Step-4: Factors of 33705

List of positive integer factors of 33705 that divides 33689 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 107, 315, 321, 535, 749, 963, 1605, 2247, 3745, 4815, 6741, 11235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33689 and 33705. The biggest common factor number is the GCF number.
So the greatest common factor 33689 and 33705 is 1.

Also check out the Least Common Multiple of 33689 and 33705