Question

If the HCF of 85 and 153 is expressed in the form 85n – 153, then the value of n is

Answer 1

Given:

Two numbers 85 and 153.

HCF of the numbers is represented as $85n - 153$.

To find:

n = ?

Solution:

Let us calculate the HCF i.e. Highest Common Factor between the two numbers.

Let us factorize the numbers:

$85 = 5 \times \underline{17}$

$153 = 3 \times 3 \times \underline{17}$

The common factors are underlined as shown above.

The highest common factor to the given numbers is 17.

$\therefore$ HCF of 85 and 153 is 17.

We are given that HCF of the two numbers is expressed as $85n - 153$.

Putting $85n - 153$ equal to 17 and finding the value of n.

$85n - 153 = 17\\\Rightarrow 85n = 17+ 153\\\Rightarrow 85n = 170\\\Rightarrow n = \dfrac{170}{85}\\\Rightarrow n = 2$

Hence, the value of n is 2.