What is the Greatest Common Factor of 51834 and 51849?

Greatest common factor (GCF) of 51834 and 51849 is 3.

GCF(51834,51849) = 3

We will now calculate the prime factors of 51834 and 51849, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51834 and 51849.

How to find the GCF of 51834 and 51849?

We will first find the prime factorization of 51834 and 51849. After we will calculate the factors of 51834 and 51849 and find the biggest common factor number .

Step-1: Prime Factorization of 51834

Prime factors of 51834 are 2, 3, 53, 163. Prime factorization of 51834 in exponential form is:

51834 = 2¹ × 3¹ × 53¹ × 163¹

Step-2: Prime Factorization of 51849

Prime factors of 51849 are 3, 7, 823. Prime factorization of 51849 in exponential form is:

51849 = 3² × 7¹ × 823¹

Step-3: Factors of 51834

List of positive integer factors of 51834 that divides 51834 without a remainder.

1, 2, 3, 6, 53, 106, 159, 163, 318, 326, 489, 978, 8639, 17278, 25917

Step-4: Factors of 51849

List of positive integer factors of 51849 that divides 51834 without a remainder.

1, 3, 7, 9, 21, 63, 823, 2469, 5761, 7407, 17283

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51834 and 51849. The biggest common factor number is the GCF number.
So the greatest common factor 51834 and 51849 is 3.

Also check out the Least Common Multiple of 51834 and 51849