What is the Greatest Common Factor of 34704 and 34719?

Greatest common factor (GCF) of 34704 and 34719 is 3.

GCF(34704,34719) = 3

We will now calculate the prime factors of 34704 and 34719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34704 and 34719.

How to find the GCF of 34704 and 34719?

We will first find the prime factorization of 34704 and 34719. After we will calculate the factors of 34704 and 34719 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34719

Prime factors of 34719 are 3, 71, 163. Prime factorization of 34719 in exponential form is:

34719 = 3¹ × 71¹ × 163¹

Step-3: Factors of 34704

List of positive integer factors of 34704 that divides 34704 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

Step-4: Factors of 34719

List of positive integer factors of 34719 that divides 34704 without a remainder.

1, 3, 71, 163, 213, 489, 11573

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34704 and 34719. The biggest common factor number is the GCF number.
So the greatest common factor 34704 and 34719 is 3.

Also check out the Least Common Multiple of 34704 and 34719