What is the Greatest Common Factor of 34689 and 34704?

Greatest common factor (GCF) of 34689 and 34704 is 3.

GCF(34689,34704) = 3

We will now calculate the prime factors of 34689 and 34704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34689 and 34704.

How to find the GCF of 34689 and 34704?

We will first find the prime factorization of 34689 and 34704. After we will calculate the factors of 34689 and 34704 and find the biggest common factor number .

Step-1: Prime Factorization of 34689

Prime factors of 34689 are 3, 31, 373. Prime factorization of 34689 in exponential form is:

34689 = 3¹ × 31¹ × 373¹

Step-2: Prime Factorization of 34704

Prime factors of 34704 are 2, 3, 241. Prime factorization of 34704 in exponential form is:

34704 = 2⁴ × 3² × 241¹

Step-3: Factors of 34689

List of positive integer factors of 34689 that divides 34689 without a remainder.

1, 3, 31, 93, 373, 1119, 11563

Step-4: Factors of 34704

List of positive integer factors of 34704 that divides 34689 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 241, 482, 723, 964, 1446, 1928, 2169, 2892, 3856, 4338, 5784, 8676, 11568, 17352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34689 and 34704. The biggest common factor number is the GCF number.
So the greatest common factor 34689 and 34704 is 3.

Also check out the Least Common Multiple of 34689 and 34704