What is the Greatest Common Factor of 3825 and 3834?

Greatest common factor (GCF) of 3825 and 3834 is 9.

GCF(3825,3834) = 9

We will now calculate the prime factors of 3825 and 3834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3825 and 3834.

How to find the GCF of 3825 and 3834?

We will first find the prime factorization of 3825 and 3834. After we will calculate the factors of 3825 and 3834 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 3834

Prime factors of 3834 are 2, 3, 71. Prime factorization of 3834 in exponential form is:

3834 = 2¹ × 3³ × 71¹

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 3834

List of positive integer factors of 3834 that divides 3825 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 71, 142, 213, 426, 639, 1278, 1917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3825 and 3834. The biggest common factor number is the GCF number.
So the greatest common factor 3825 and 3834 is 9.

Also check out the Least Common Multiple of 3825 and 3834