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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

3. Zero is a multiple of every non-zero number. FACTS test oF divisiBility
examples: 3 × 0 = 0, 5 × 0 = 0, 72 × 0 = 0, etc. If a number is a multiple
A number
4. Every multiple of a given number is greater than or equal of a given number, the is divisible divisibility rule examples
number will be completely
to the number. divisible by the given by
example: Multiples of 3 are 3, 6, 9, 12, ... number.
5. There are an infinite number of multiples of a number. 2 if the digit in its ones place is 0, 2, 4, 252, 1484, 5498 and 3200 are divisible by
example: Multiples of 5 are 5, 10, 15, 20, 25, 30, ... 6 or 8. 2.

6. The smallest multiple of a number is the number itself. 3 if the sum of the digits of a number 6381 is divisible by 3. (6 + 3 + 8 + 1 = 18,
and 18 ÷ 3 = 6)
is divisible by 3.
7. The multiples of an even number are always even numbers.
examples: (a) Multiples of 2 are 2, 4, 6, 8, 10, … which are even numbers. 4 if the number formed by the last two 328 is divisible by 4. The number formed
digits (tens and ones digits) of the
by the last 2 digits is divisible by 4, i.e.,
(b) Multiples of 8 are 8, 16, 24, 32, … which are even numbers. number is divisible by 4. 28 ÷ 4 = 7.
8. The multiples of an odd number are alternately an odd and an even number. if the digit in its ones place is either
example: Multiples of 3 are 3, 6, 9, 12, 15, …, where 3, 9, 15, … are odd numbers 5 0 or 5. 475, 500 and 2555 are divisible by 5.

and 6, 12, … are even numbers.
3144 is divisible by 6. As 3 + 1 + 4 + 4 =
if the number is divisible by both 2 12 which is divisible by 3. The digit in the
6
Think Tank Critical Thinking and 3. ones place is 4. Therefore 3144 is divisible
How many multiples of 13 are there between 100 and 200? by 2.
if the number formed by the last 4328 is divisible by 8. The number formed
Practice time 3B 8 three digits (hundreds, tens and ones by the last 3 digits is divisible by 8, i.e.,
digits) of the number is divisible by 8. 328 ÷ 8 = 41.
1. Fill in the blanks. if the sum of the digits of a number 6192 is divisible by 9. 6 + 1 + 9 + 2 = 18,
( a) _________ is the smallest multiple of 7. 9 is divisible by 9. which is divisible by 9.

( b) Multiples of an even number are ________ numbers. 10 if the digit in the ones place is 0. 1050, 3000 and 5500 are divisible by 10.
( c) Every number is a multiple of ________ and ________.
( d) ______ is the multiple of every non-zero number. if the difference of the sum of the 25861 is divisible by 11.
digits in the odd places and the sum
( e) There are __________ multiples of 10 between 1 and 100. 11 of the digits in the even places is [(2 + 8 + 1) – (5 + 6)] = (11 – 11) = 0

2. Find the first five multiples of: either 0 or divisible by 11.
( a) 11 (b) 13 (c) 18 (d) 24 (e) 75 Subject Enrichment
3. Find:
th
( a) the 8 multiple of 48. (b) the 10 multiple of 50. A number is divisible by 7, if the difference between twice the ones
th
th
( c) the 12 multiple of 96. (d) the first five even multiples of 9. digit of the given number and the remaining part of the given number 383 6
( e) the first five odd multiples of 11. is a multiple of 7 or is equal to 0.
4. Find the multiples of: For example: 3836 is divisible by 7. 6 × 2 = 12

( a) 11 that are less than 200. (b) 25 between 100 and 220. 383 – 2 × 6 = 383 – 12 = 371 and 371 ÷ 7 = 53. 383 – 12 = 371
( c) 19 between 140 and 160. (d) 15 which are 2-digit numbers.
5. Check the following.
( a) Is 238 a multiple of 8? (b) Is 196 a multiple of 16? Think Tank Logical Thinking

( c) Is 386 a multiple of 9? (d) Is 1440 a multiple of 12? What is the pin code of your area? Is your area pin code divisible by 11? Cross-Curricular Learning

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