What is the Greatest Common Factor of 10704 and 10719?

Greatest common factor (GCF) of 10704 and 10719 is 3.

GCF(10704,10719) = 3

We will now calculate the prime factors of 10704 and 10719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10704 and 10719.

How to find the GCF of 10704 and 10719?

We will first find the prime factorization of 10704 and 10719. After we will calculate the factors of 10704 and 10719 and find the biggest common factor number .

Step-1: Prime Factorization of 10704

Prime factors of 10704 are 2, 3, 223. Prime factorization of 10704 in exponential form is:

10704 = 2⁴ × 3¹ × 223¹

Step-2: Prime Factorization of 10719

Prime factors of 10719 are 3, 397. Prime factorization of 10719 in exponential form is:

10719 = 3³ × 397¹

Step-3: Factors of 10704

List of positive integer factors of 10704 that divides 10704 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 223, 446, 669, 892, 1338, 1784, 2676, 3568, 5352

Step-4: Factors of 10719

List of positive integer factors of 10719 that divides 10704 without a remainder.

1, 3, 9, 27, 397, 1191, 3573

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10704 and 10719. The biggest common factor number is the GCF number.
So the greatest common factor 10704 and 10719 is 3.

Also check out the Least Common Multiple of 10704 and 10719