(iii) Step 1: Choose bigger number : 1575 > 960
 
On dividing $1575$ by $90$ , we have
quotient $=1$ remainder $=615$
$\Rightarrow$1575 = 960$\times$1 +615$$

Step 2 : on Dividing $960$ by $615$ , we have

Quotient $=1$ and remainder $=345$ 
$\Rightarrow ,960=615\times 1+345$

Step 3 :on dividing $615$ by $345$
quotient $1$ and remainder $=270$

$\Rightarrow 615=345\times 1+270$

Step 4 : On dividing $345$ by $270$ , we have 

quotient $=1$ and remainder $=75$ 
$\Rightarrow 345=270\times 1+75$

Step 5 : dividing $270$ by $75$ , we get
Quotient$=3$, remainder $=30$
$\Rightarrow 270=75\times +45$

Step 6 : Dividing $75$ by $45$ we get

Quotient $=1$, remainder $=30$

$\Rightarrow 75=45\times 1+30$

Step 7: Dividing $45$ by $30$ , we get

quotient $=1$ and remainder $=15$

$\Rightarrow 45=30\times 1+15$

Step 8 :  Dividing $30$  by $15$ , we get

quotient $=2$ and remainder $=0$

Since remainder is zero, stop the process 

Therefore , HCF of $1575$ and $960$ is $15.$