What is the Greatest Common Factor of 25740 and 25753?

Greatest common factor (GCF) of 25740 and 25753 is 13.

GCF(25740,25753) = 13

We will now calculate the prime factors of 25740 and 25753, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25740 and 25753.

How to find the GCF of 25740 and 25753?

We will first find the prime factorization of 25740 and 25753. After we will calculate the factors of 25740 and 25753 and find the biggest common factor number .

Step-1: Prime Factorization of 25740

Prime factors of 25740 are 2, 3, 5, 11, 13. Prime factorization of 25740 in exponential form is:

25740 = 2² × 3² × 5¹ × 11¹ × 13¹

Step-2: Prime Factorization of 25753

Prime factors of 25753 are 7, 13, 283. Prime factorization of 25753 in exponential form is:

25753 = 7¹ × 13¹ × 283¹

Step-3: Factors of 25740

List of positive integer factors of 25740 that divides 25740 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 18, 20, 22, 26, 30, 33, 36, 39, 44, 45, 52, 55, 60, 65, 66, 78, 90, 99, 110, 117, 130, 132, 143, 156, 165, 180, 195, 198, 220, 234, 260, 286, 330, 390, 396, 429, 468, 495, 572, 585, 660, 715, 780, 858, 990, 1170, 1287, 1430, 1716, 1980, 2145, 2340, 2574, 2860, 4290, 5148, 6435, 8580, 12870

Step-4: Factors of 25753

List of positive integer factors of 25753 that divides 25740 without a remainder.

1, 7, 13, 91, 283, 1981, 3679

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25740 and 25753. The biggest common factor number is the GCF number.
So the greatest common factor 25740 and 25753 is 13.

Also check out the Least Common Multiple of 25740 and 25753