What is the Greatest Common Factor of 25830 and 25840?

Greatest common factor (GCF) of 25830 and 25840 is 10.

GCF(25830,25840) = 10

We will now calculate the prime factors of 25830 and 25840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25830 and 25840.

How to find the GCF of 25830 and 25840?

We will first find the prime factorization of 25830 and 25840. After we will calculate the factors of 25830 and 25840 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 25840

Prime factors of 25840 are 2, 5, 17, 19. Prime factorization of 25840 in exponential form is:

25840 = 2⁴ × 5¹ × 17¹ × 19¹

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 25840

List of positive integer factors of 25840 that divides 25830 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 19, 20, 34, 38, 40, 68, 76, 80, 85, 95, 136, 152, 170, 190, 272, 304, 323, 340, 380, 646, 680, 760, 1292, 1360, 1520, 1615, 2584, 3230, 5168, 6460, 12920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25830 and 25840. The biggest common factor number is the GCF number.
So the greatest common factor 25830 and 25840 is 10.

Also check out the Least Common Multiple of 25830 and 25840