What is the Greatest Common Factor of 54825 and 54842?

Greatest common factor (GCF) of 54825 and 54842 is 17.

GCF(54825,54842) = 17

We will now calculate the prime factors of 54825 and 54842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54825 and 54842.

How to find the GCF of 54825 and 54842?

We will first find the prime factorization of 54825 and 54842. After we will calculate the factors of 54825 and 54842 and find the biggest common factor number .

Step-1: Prime Factorization of 54825

Prime factors of 54825 are 3, 5, 17, 43. Prime factorization of 54825 in exponential form is:

54825 = 3¹ × 5² × 17¹ × 43¹

Step-2: Prime Factorization of 54842

Prime factors of 54842 are 2, 17, 1613. Prime factorization of 54842 in exponential form is:

54842 = 2¹ × 17¹ × 1613¹

Step-3: Factors of 54825

List of positive integer factors of 54825 that divides 54825 without a remainder.

1, 3, 5, 15, 17, 25, 43, 51, 75, 85, 129, 215, 255, 425, 645, 731, 1075, 1275, 2193, 3225, 3655, 10965, 18275

Step-4: Factors of 54842

List of positive integer factors of 54842 that divides 54825 without a remainder.

1, 2, 17, 34, 1613, 3226, 27421

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54825 and 54842. The biggest common factor number is the GCF number.
So the greatest common factor 54825 and 54842 is 17.

Also check out the Least Common Multiple of 54825 and 54842