Spending time on such an exercise not only reduces your chances of answering the problem within the two-minute time frame but is also inefficient: long division will tell you the result of dividing 5,142,376,298 by 3 when all you really need to know is whether it is divisible.

To answer that, we need to discuss the rules of divisibility. This is a collection of rules that can help you quickly decide whether an integer is divisible by a smaller integer, without going through the tedious exercise of actually calculating the result. We will, of course, confine the subject to rules of divisibility by the few integers that are typically required to solve questions:

2, 3, 4, 5, 6, 8, 9, 10

Rule of divisibility by 2 – well, that’s easy. An integer is divisible by 2 if its last digit (the unit’s digit) is divisible by 2. (Remember, divisible means that the result is an integer.)

So 1,456 is divisible by 2, because its last digit is 6, which is divisible by 2.

Similarly, 2,390,399 is not divisible by 2, because its last digit is 9, which is not divisible by 2.

Rule of divisibility by 3 – An integer is divisible by 3 if the sum of its digits is divisible by 3.

So 1,455 is divisible by 3, because 1+4+5+5=15, which is divisible by 3.

Similarly, 13,934 is not divisible by 3, because 1+3+9+3+4=20, which is not divisible by 3.

An integer is divisible by 4 if its last two digits form a two-digit number that is divisible by 4.

For example, 12,560 is divisible by 4, because its last two digits form a number (60) that is divisible by 4.

The Rule of divisibility by 5 is an easy one – an integer is divisible by 5 if its last digit is either 5 or 0.

For example, both 560 and 12,345 are divisible by 5, because their units digit are 5 and 0, respectively.

The Rule of divisibility by 6 is interesting because it relies on other rules we’ve seen before. Simply put, an integer is divisible by 6 if it is divisible by 2 and 3. So if an integer clears the conditions set for divisibility by 2 and 3, it is also divisible by 6.

For example, 23,424 is divisible by 6, because it satisfies both conditions:

• Its unit’s digit is 4, which is divisible by 2.

AND

• The sum of its digits (2+3+4+2+4 = 15) is divisible by 3, so it’s also divisible by 3.

Rule of divisibility by 8 – an integer is divisible by 8 if its last 3 digits form a 3-digit number that is divisible by 8.

For example, 3,242,353,720 is divisible by 8, because 720 is divisible by 8.

You can just use a calculator to divide the 3-digit number by 8.

Rule of divisibility by 9 – An integer is divisible by 9 if the sum of its digits is divisible by 9.

So 1,458 is divisible by 9, because 1+4+5+8=18, which is divisible by 9.

Note that this rule is quite similar to the rule of divisibility by 3 (sum of digits must be divisible by 3), but with the condition that the sum of digits must be divisible by 9.

An integer may NOT be divisible by 9, yet still, be divisible by 3.

For example, is 4,380 divisible by 9?

Add up the digits (4+3+8+0) = 15, which is NOT divisible by 9.

But is 4,380 divisible by 3? Why, yes indeed, because the sum of the digits (15) is divisible by 3.

Rule of divisibility by 10

This is the easiest of all rules of divisibility – an integer is divisible by 10 if its last digit (unit’s digit) is Zero. That’s it.

For example,

• 480
• 15,720
• 1,000,000,000
  are all divisible by 10, because their last (units digit) is 0.