What is the Greatest Common Factor of 25690 and 25704?

Greatest common factor (GCF) of 25690 and 25704 is 14.

GCF(25690,25704) = 14

We will now calculate the prime factors of 25690 and 25704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25690 and 25704.

How to find the GCF of 25690 and 25704?

We will first find the prime factorization of 25690 and 25704. After we will calculate the factors of 25690 and 25704 and find the biggest common factor number .

Step-1: Prime Factorization of 25690

Prime factors of 25690 are 2, 5, 7, 367. Prime factorization of 25690 in exponential form is:

25690 = 2¹ × 5¹ × 7¹ × 367¹

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 25690

List of positive integer factors of 25690 that divides 25690 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 367, 734, 1835, 2569, 3670, 5138, 12845

Step-4: Factors of 25704

List of positive integer factors of 25704 that divides 25690 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 25690 and 25704. The biggest common factor number is the GCF number.
So the greatest common factor 25690 and 25704 is 14.

Also check out the Least Common Multiple of 25690 and 25704