What is the Greatest Common Factor of 25730 and 25740?

Greatest common factor (GCF) of 25730 and 25740 is 10.

GCF(25730,25740) = 10

We will now calculate the prime factors of 25730 and 25740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25730 and 25740.

How to find the GCF of 25730 and 25740?

We will first find the prime factorization of 25730 and 25740. After we will calculate the factors of 25730 and 25740 and find the biggest common factor number .

Step-1: Prime Factorization of 25730

Prime factors of 25730 are 2, 5, 31, 83. Prime factorization of 25730 in exponential form is:

25730 = 2¹ × 5¹ × 31¹ × 83¹

Step-2: 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-3: Factors of 25730

List of positive integer factors of 25730 that divides 25730 without a remainder.

1, 2, 5, 10, 31, 62, 83, 155, 166, 310, 415, 830, 2573, 5146, 12865

Step-4: Factors of 25740

List of positive integer factors of 25740 that divides 25730 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25730 and 25740. The biggest common factor number is the GCF number.
So the greatest common factor 25730 and 25740 is 10.

Also check out the Least Common Multiple of 25730 and 25740