What is the Greatest Common Factor of 19805 and 19825?

Greatest common factor (GCF) of 19805 and 19825 is 5.

GCF(19805,19825) = 5

We will now calculate the prime factors of 19805 and 19825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19805 and 19825.

How to find the GCF of 19805 and 19825?

We will first find the prime factorization of 19805 and 19825. After we will calculate the factors of 19805 and 19825 and find the biggest common factor number .

Step-1: Prime Factorization of 19805

Prime factors of 19805 are 5, 17, 233. Prime factorization of 19805 in exponential form is:

19805 = 5¹ × 17¹ × 233¹

Step-2: 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-3: Factors of 19805

List of positive integer factors of 19805 that divides 19805 without a remainder.

1, 5, 17, 85, 233, 1165, 3961

Step-4: Factors of 19825

List of positive integer factors of 19825 that divides 19805 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19805 and 19825. The biggest common factor number is the GCF number.
So the greatest common factor 19805 and 19825 is 5.

Also check out the Least Common Multiple of 19805 and 19825