What is the Greatest Common Factor of 19825 and 19830?

Greatest common factor (GCF) of 19825 and 19830 is 5.

GCF(19825,19830) = 5

We will now calculate the prime factors of 19825 and 19830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19825 and 19830.

How to find the GCF of 19825 and 19830?

We will first find the prime factorization of 19825 and 19830. After we will calculate the factors of 19825 and 19830 and find the biggest common factor number .

Step-1: Prime Factorization of 19825

Prime factors of 19825 are 5, 13, 61. Prime factorization of 19825 in exponential form is:

19825 = 5² × 13¹ × 61¹

Step-2: Prime Factorization of 19830

Prime factors of 19830 are 2, 3, 5, 661. Prime factorization of 19830 in exponential form is:

19830 = 2¹ × 3¹ × 5¹ × 661¹

Step-3: Factors of 19825

List of positive integer factors of 19825 that divides 19825 without a remainder.

1, 5, 13, 25, 61, 65, 305, 325, 793, 1525, 3965

Step-4: Factors of 19830

List of positive integer factors of 19830 that divides 19825 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 661, 1322, 1983, 3305, 3966, 6610, 9915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19825 and 19830. The biggest common factor number is the GCF number.
So the greatest common factor 19825 and 19830 is 5.

Also check out the Least Common Multiple of 19825 and 19830