What is the Greatest Common Factor of 25700 and 25704?

Greatest common factor (GCF) of 25700 and 25704 is 4.

GCF(25700,25704) = 4

We will now calculate the prime factors of 25700 and 25704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25700 and 25704.

How to find the GCF of 25700 and 25704?

We will first find the prime factorization of 25700 and 25704. After we will calculate the factors of 25700 and 25704 and find the biggest common factor number .

Step-1: Prime Factorization of 25700

Prime factors of 25700 are 2, 5, 257. Prime factorization of 25700 in exponential form is:

25700 = 2² × 5² × 257¹

Step-2: 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-3: Factors of 25700

List of positive integer factors of 25700 that divides 25700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 257, 514, 1028, 1285, 2570, 5140, 6425, 12850

Step-4: Factors of 25704

List of positive integer factors of 25704 that divides 25700 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25700 and 25704. The biggest common factor number is the GCF number.
So the greatest common factor 25700 and 25704 is 4.

Also check out the Least Common Multiple of 25700 and 25704