What is the Greatest Common Factor of 15742 and 15759?

Greatest common factor (GCF) of 15742 and 15759 is 17.

GCF(15742,15759) = 17

We will now calculate the prime factors of 15742 and 15759, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15742 and 15759.

How to find the GCF of 15742 and 15759?

We will first find the prime factorization of 15742 and 15759. After we will calculate the factors of 15742 and 15759 and find the biggest common factor number .

Step-1: Prime Factorization of 15742

Prime factors of 15742 are 2, 17, 463. Prime factorization of 15742 in exponential form is:

15742 = 2¹ × 17¹ × 463¹

Step-2: Prime Factorization of 15759

Prime factors of 15759 are 3, 17, 103. Prime factorization of 15759 in exponential form is:

15759 = 3² × 17¹ × 103¹

Step-3: Factors of 15742

List of positive integer factors of 15742 that divides 15742 without a remainder.

1, 2, 17, 34, 463, 926, 7871

Step-4: Factors of 15759

List of positive integer factors of 15759 that divides 15742 without a remainder.

1, 3, 9, 17, 51, 103, 153, 309, 927, 1751, 5253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15742 and 15759. The biggest common factor number is the GCF number.
So the greatest common factor 15742 and 15759 is 17.

Also check out the Least Common Multiple of 15742 and 15759