What is the Greatest Common Factor of 3825 and 3842?

Greatest common factor (GCF) of 3825 and 3842 is 17.

GCF(3825,3842) = 17

We will now calculate the prime factors of 3825 and 3842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3825 and 3842.

How to find the GCF of 3825 and 3842?

We will first find the prime factorization of 3825 and 3842. After we will calculate the factors of 3825 and 3842 and find the biggest common factor number .

Step-1: Prime Factorization of 3825

Prime factors of 3825 are 3, 5, 17. Prime factorization of 3825 in exponential form is:

3825 = 3² × 5² × 17¹

Step-2: Prime Factorization of 3842

Prime factors of 3842 are 2, 17, 113. Prime factorization of 3842 in exponential form is:

3842 = 2¹ × 17¹ × 113¹

Step-3: Factors of 3825

List of positive integer factors of 3825 that divides 3825 without a remainder.

1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275

Step-4: Factors of 3842

List of positive integer factors of 3842 that divides 3825 without a remainder.

1, 2, 17, 34, 113, 226, 1921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3825 and 3842. The biggest common factor number is the GCF number.
So the greatest common factor 3825 and 3842 is 17.

Also check out the Least Common Multiple of 3825 and 3842