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Chapter 15: Playing with Numbers

    Introduction

    Divisibility Rules

    Some More Divisibility Rules

    Puzzles Based on Divisibility Rules

    Fun with 3-Digit Numbers

    Puzzles with Missing Digits

    Finding of Divisibility by taking Remainders of Place Values

    Some More Puzzles on Divisibility Rules

    Finding Sum of Consecutive Numbers

    Exercise 15.1

    Exercise 15.2

    Exercise 15.3

    Exercise 15.4

    Exercise 15.5

    Exercise 15.6

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 15: Playing with Numbers > Some More Divisibility Rules

Some More Divisibility Rules

If a number is divisible by another number, it is also divisible by its factors.

A number divisible by 6 is also divisible by and , because 6 = 2 × 3. Eg: 72 is divisible by 6, so it must also be divisible by 2 and 3.

Simiarly, a number divisible by 12 is also divisible by 3 and 4, because 12 = × . Example: 144 is divisible by 12, so it must also be divisible by 3 and 4.

If a number is divisible by two coprime numbers, then it is divisible by their product. Two numbers are coprime if they have no common factors other than 1.

If a number is divisible by 4 and 9, then it is also divisible by , because × = .

Similarly, if a number is divisible by 5 and 8, then it is also divisible by , because × = .

If two numbers are divisible by the same number, then their sum is also divisible by that number.

Let’s take two numbers 24 and 36, both of which are divisible by 6:

24 ÷ 6 =

36 ÷ 6 =

Now, let’s find their sum: 24 + 36 =

Since, this number is also divisible by 6: ÷ 6 =

If two numbers are divisible by the same number, then their difference is also divisible by that number.

Using the same numbers, 24 and 36, both divisible by :

Now, let's find their difference: 36 − 24 =

Since, this number is also divisible by 6: ÷ 6 =