Page 97 - Math Genius C4

E:\Working\Orange_Education\Math_Genius_4\Open_Files\Chap-05
\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

Properties of Multiples Practice time 5B

1. Every number other than zero is a multiple of itself. 1. Find the first six multiples of:

Examples: Multiples of 4 are 4, 8, 12, 16, ... (a) 5 (b) 7 (c) 11 (d) 13
Multiples of 5 are 5, 10, 15, 20, ... 2. Write the first five even multiples of:

Clearly, 4 and 5 are multiples of themselves. (a) 17 (b) 13 (c) 15 (d) 25

2. Every multiple of a number other than zero is greater than or equal to itself. 3. Write the following.
Examples: Multiples of 6 are 6, 12, 18, 24, ... (a) The 5th multiple of 8 (b) The 8th multiple of 9

Multiples of 7 are 7, 14, 21, 28, ...
Think Tank Logical Thinking (c) Multiples of 12 less than 144 (d) Multiples of 3 between 20 and 50
3. There are an infinite (endless or uncountable) List the first five (e) Multiples of 9 between 50 and 100

number of multiples of a number. multiples of your age and
Examples: Multiples of 7 are 7, 14, 21, 28, ... your friend’s age taking complete (f) The first multiple of 9 which is exactly divisible by 8.
years.
Multiples of 9 are 9, 18, 27, 36, ... 4. Find the first four common multiples of the following numbers. Then circle
Multiples of 10 are 10, 20, 30, 40, ... the smallest common multiple.

From the above examples, we can say that there are infinite multiples of any given (a) 4 and 5 (b) 3 and 5 (c) 2 and 7 (d) 6 and 8 (e) 10 and 20
number. test oF DivisiBility

common Multiples 1 2 3 4 5 6 7 8 9 10 When we divide a number by another number and we get 0 as the remainder, then

Here the numbers 1 to 60 are shown in 11 12 13 14 15 16 17 18 19 20 the number is called divisible by the other number.
the grid. We circle those numbers red 21 22 23 24 25 26 27 28 29 30 Let us divide both 85 and 88 by 5.
which are the multiples of 4 and blue 31 32 33 34 35 36 37 38 39 40 On dividing 85 by 5, we get the remainder 0. 5 85 17 5 88 17
5
which are the multiples of 6. So, 85 is divisible by 5. 5 38
35
Numbers in red circles are: 4, 8, 12, 16, 20, 41 42 43 44 45 46 47 48 49 50 35 35

24, 28, 32, 36, 40, 44, 48, 52, 56 and 60. 51 52 53 54 55 56 57 58 59 60 On dividing 88 by 5, we get the remainder 3 instead of 0. 0 3
Numbers in blue circles are: 6, 12, 18, 24, 30, 36, 42, 48, 54 and 60. So, 88 is not divisible by 5.

Numbers in both coloured circles are: 12, 24, 36, 48 and 60. There are certain tests or rules using which we can tell whether a number is divisible
by another number or not without actually performing the division.
Thus, the common multiples of 4 and 6 are 12, 24, 36, 48 and 60. Divisibility by 2

Hence, the numbers which are common among rule: All even numbers are divisible by 2. This means that numbers ending in 0, 2,
the multiples of two or more numbers are called Think Tank Logical Thinking 4, 6 and 8 are divisible by 2.
the common multiples. There are 7 days in Examples: 10, 256, 3498 are divisible by 2.

Example: Find the common multiples of 2 and 5. a week. Which of the
following numbers of days will Divisibility by 3
Solution: The multiples of 2 are 2, 4, 6, 8, 10 , form an exact number of weeks? rule: If the sum of all the digits of a number is divisible by 3, then the number

12, 14, 16, 18, 20 , ... 7, 10, 13, 14, 20, 23, 28, 31 itself is divisible by 3.
The multiples of 5 are 5, 10 , 15, 20 , 25, 30, 35, ... Example: In 24, 2 + 4 = 6 and 6 ÷ 3 = 2

The common multiples of 2 and 5 are 10, 20, ... So, 24 is divisible by 3.

Mathematics-4 95