What is the Greatest Common Factor of 25830 and 25842?

Greatest common factor (GCF) of 25830 and 25842 is 6.

GCF(25830,25842) = 6

We will now calculate the prime factors of 25830 and 25842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25830 and 25842.

How to find the GCF of 25830 and 25842?

We will first find the prime factorization of 25830 and 25842. After we will calculate the factors of 25830 and 25842 and find the biggest common factor number .

Step-1: Prime Factorization of 25830

Prime factors of 25830 are 2, 3, 5, 7, 41. Prime factorization of 25830 in exponential form is:

25830 = 2¹ × 3² × 5¹ × 7¹ × 41¹

Step-2: Prime Factorization of 25842

Prime factors of 25842 are 2, 3, 59, 73. Prime factorization of 25842 in exponential form is:

25842 = 2¹ × 3¹ × 59¹ × 73¹

Step-3: Factors of 25830

List of positive integer factors of 25830 that divides 25830 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 41, 42, 45, 63, 70, 82, 90, 105, 123, 126, 205, 210, 246, 287, 315, 369, 410, 574, 615, 630, 738, 861, 1230, 1435, 1722, 1845, 2583, 2870, 3690, 4305, 5166, 8610, 12915

Step-4: Factors of 25842

List of positive integer factors of 25842 that divides 25830 without a remainder.

1, 2, 3, 6, 59, 73, 118, 146, 177, 219, 354, 438, 4307, 8614, 12921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25830 and 25842. The biggest common factor number is the GCF number.
So the greatest common factor 25830 and 25842 is 6.

Also check out the Least Common Multiple of 25830 and 25842