**Q1. Show that 52563744 is divisible by 24 ?**

A. To check the divisibility of 52563744 by 24, we need to ensure that our given number is divisible by 3 and 8 both.

Checking divisibility by 3:

Sum of digits of number : 36, divisible by 3.

Checking divisibility by 8:

Number formed by last 3 digits – 744, divisible by 8.

Hence, we see that given number is divisible by both 3 and 8, and hence, will be divisible by 24.

**Q2. Find the least number that should be subtracted from 1672 to obtain a number which is completely divisible by 17 ?**

A. On dividing 1672 by 17, you will get 6 as a remainder. That is our least number that must be subtracted.

**Q3. Find the least number that should be added to 2010 to obtain a number which is completely divisible by 19 ?**

A. On dividing 2010 by 19, you will get 15 as a remainder. So, required number is 19-15 = 4

**Q4. On dividing a number by 342, we get 47 as remainder. If same number is divided by 18, then find the remainder.**

A. Let the quotient be ‘x’. Then, on applying formula

Divisor = (Dividend – Remainder)/Quotient

Number = 342x + 47

=> (18 * 19x) + (18 * 2) + 11

=> 18 + (19x + 2) + 11

So, number when divided by 18 gives remainder 11.

**Q5. Find the least value of * for which 684*628 is divisible by 12 ?**

A. **Divisibility by 12 :**

A number is divisible by 12, if and only if it can be divided by 3 and 4 both.

**Checking for divisibility by 3 :**

A number is divisible by 3 only when the sum of its digits is divisible by 3.

So, 6 + 8 + 4 + * + 6 + 2 + 8 = 34 + *

Value of * may be 2, 5, 8 etc.

**Checking for divisibility by 4 :**

A number is divisible by 4 if and only if its last two digits is divisible by 4.

28 is divisible by 4.

So, least value is **2**.