What is the Greatest Common Factor of 15725 and 15742?

Greatest common factor (GCF) of 15725 and 15742 is 17.

GCF(15725,15742) = 17

We will now calculate the prime factors of 15725 and 15742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15725 and 15742.

How to find the GCF of 15725 and 15742?

We will first find the prime factorization of 15725 and 15742. After we will calculate the factors of 15725 and 15742 and find the biggest common factor number .

Step-1: Prime Factorization of 15725

Prime factors of 15725 are 5, 17, 37. Prime factorization of 15725 in exponential form is:

15725 = 5² × 17¹ × 37¹

Step-2: 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-3: Factors of 15725

List of positive integer factors of 15725 that divides 15725 without a remainder.

1, 5, 17, 25, 37, 85, 185, 425, 629, 925, 3145

Step-4: Factors of 15742

List of positive integer factors of 15742 that divides 15725 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15725 and 15742. The biggest common factor number is the GCF number.
So the greatest common factor 15725 and 15742 is 17.

Also check out the Least Common Multiple of 15725 and 15742