What is the Greatest Common Factor of 9825 and 9840?

Greatest common factor (GCF) of 9825 and 9840 is 15.

GCF(9825,9840) = 15

We will now calculate the prime factors of 9825 and 9840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9825 and 9840.

How to find the GCF of 9825 and 9840?

We will first find the prime factorization of 9825 and 9840. After we will calculate the factors of 9825 and 9840 and find the biggest common factor number .

Step-1: Prime Factorization of 9825

Prime factors of 9825 are 3, 5, 131. Prime factorization of 9825 in exponential form is:

9825 = 3¹ × 5² × 131¹

Step-2: Prime Factorization of 9840

Prime factors of 9840 are 2, 3, 5, 41. Prime factorization of 9840 in exponential form is:

9840 = 2⁴ × 3¹ × 5¹ × 41¹

Step-3: Factors of 9825

List of positive integer factors of 9825 that divides 9825 without a remainder.

1, 3, 5, 15, 25, 75, 131, 393, 655, 1965, 3275

Step-4: Factors of 9840

List of positive integer factors of 9840 that divides 9825 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41, 48, 60, 80, 82, 120, 123, 164, 205, 240, 246, 328, 410, 492, 615, 656, 820, 984, 1230, 1640, 1968, 2460, 3280, 4920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9825 and 9840. The biggest common factor number is the GCF number.
So the greatest common factor 9825 and 9840 is 15.

Also check out the Least Common Multiple of 9825 and 9840