What is the Greatest Common Factor of 9825 and 9842?

Greatest common factor (GCF) of 9825 and 9842 is 1.

GCF(9825,9842) = 1

We will now calculate the prime factors of 9825 and 9842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9825 and 9842.

How to find the GCF of 9825 and 9842?

We will first find the prime factorization of 9825 and 9842. After we will calculate the factors of 9825 and 9842 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 9842

Prime factors of 9842 are 2, 7, 19, 37. Prime factorization of 9842 in exponential form is:

9842 = 2¹ × 7¹ × 19¹ × 37¹

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 9842

List of positive integer factors of 9842 that divides 9825 without a remainder.

1, 2, 7, 14, 19, 37, 38, 74, 133, 259, 266, 518, 703, 1406, 4921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9825 and 9842. The biggest common factor number is the GCF number.
So the greatest common factor 9825 and 9842 is 1.

Also check out the Least Common Multiple of 9825 and 9842