What is the Greatest Common Factor of 25704 and 25721?

Greatest common factor (GCF) of 25704 and 25721 is 17.

GCF(25704,25721) = 17

We will now calculate the prime factors of 25704 and 25721, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25704 and 25721.

How to find the GCF of 25704 and 25721?

We will first find the prime factorization of 25704 and 25721. After we will calculate the factors of 25704 and 25721 and find the biggest common factor number .

Step-1: Prime Factorization of 25704

Prime factors of 25704 are 2, 3, 7, 17. Prime factorization of 25704 in exponential form is:

25704 = 2³ × 3³ × 7¹ × 17¹

Step-2: Prime Factorization of 25721

Prime factors of 25721 are 17, 89. Prime factorization of 25721 in exponential form is:

25721 = 17² × 89¹

Step-3: Factors of 25704

List of positive integer factors of 25704 that divides 25704 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 27, 28, 34, 36, 42, 51, 54, 56, 63, 68, 72, 84, 102, 108, 119, 126, 136, 153, 168, 189, 204, 216, 238, 252, 306, 357, 378, 408, 459, 476, 504, 612, 714, 756, 918, 952, 1071, 1224, 1428, 1512, 1836, 2142, 2856, 3213, 3672, 4284, 6426, 8568, 12852

Step-4: Factors of 25721

List of positive integer factors of 25721 that divides 25704 without a remainder.

1, 17, 89, 289, 1513

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25704 and 25721. The biggest common factor number is the GCF number.
So the greatest common factor 25704 and 25721 is 17.

Also check out the Least Common Multiple of 25704 and 25721