What is the Greatest Common Factor of 15723 and 15738?

Greatest common factor (GCF) of 15723 and 15738 is 3.

GCF(15723,15738) = 3

We will now calculate the prime factors of 15723 and 15738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15723 and 15738.

How to find the GCF of 15723 and 15738?

We will first find the prime factorization of 15723 and 15738. After we will calculate the factors of 15723 and 15738 and find the biggest common factor number .

Step-1: Prime Factorization of 15723

Prime factors of 15723 are 3, 1747. Prime factorization of 15723 in exponential form is:

15723 = 3² × 1747¹

Step-2: Prime Factorization of 15738

Prime factors of 15738 are 2, 3, 43, 61. Prime factorization of 15738 in exponential form is:

15738 = 2¹ × 3¹ × 43¹ × 61¹

Step-3: Factors of 15723

List of positive integer factors of 15723 that divides 15723 without a remainder.

1, 3, 9, 1747, 5241

Step-4: Factors of 15738

List of positive integer factors of 15738 that divides 15723 without a remainder.

1, 2, 3, 6, 43, 61, 86, 122, 129, 183, 258, 366, 2623, 5246, 7869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15723 and 15738. The biggest common factor number is the GCF number.
So the greatest common factor 15723 and 15738 is 3.

Also check out the Least Common Multiple of 15723 and 15738