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

Properties of Factors MultiPles

1. 1 is a factor of every number. Knowledge Desk Let us write the factors of 18.
examples: 1 × 5 = 5, 1 × 8 = 8, 1 × 24 = 24, etc. 18 = 1 × 18, 18 = 2 × 9 and 18 = 3 × 6

2. Every number is a factor of itself. If the sum of the factors of a Therefore, 1, 2, 3, 6, 9 and 18 are the factors of 18.
number (excluding the number
examples: 7 × 1 = 7, 9 × 1 = 9, 73 × 1 = 73, etc. itself) is equal to the number, We can say that 18 is a multiple of each of its factors (1, 2, 3, 6, 9 and 18).
3. Every non-zero number (except 1) has at least two then it is called a perfect Thus, a number is a multiple of each of its factors.
number. The first perfect
factors. 1 has only 1 factor. number is 6 as the sum of the We can define it as “A multiple of a number is obtained by multiplying it with a natural

4. There are a finite number of factors of any number. factors of 6 is 1+2+3=6. number”.
example: The factors of 30 are 1, 2, 3, 5, 6, 10, 15 The next is 28 (1+2+4+7+14=28). For example, let us multiply 4 by 1, 2, 3, 4, …, we get
Can you find the next one?
and 30. Knowledge Desk
So, the factors are limited. 4 × 1 = 4, 4 × 2 = 8, 4 × 3 = 12, 4 × 4 = 16, … Counting numbers 1,

5. Any factor of a number is equal to or less than the given Be Aware Here, we get 4, 8, 12, 16, 20, … as the multiples of 4. 2, 3, 4, 5, … are called
natural numbers.
number. 1 is the smallest factor example 1: Find the first four multiples of 5.
example: The factors of 18 are 1, 2, 3, 6, 9 and 18. of a number. Solution: We know that 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15 and 5 × 4 = 20.

6. Zero is not a factor of any number, whereas every number is a factor of zero. Thus, the first four multiples of 5 are 5, 10, 15 and 20.
th
example 2: Find the 13 multiple of 12.
Think Tank Critical Thinking
Solution: We know that 12 × 13 = 156.
Is your age a factor of the sum of your parents’ age? Thus, the 13 multiple of 12 is 156. 2 4
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example 3: Is 435 a multiple of 18? 18 4 3 5
Practice time 3a Solution: If 435 is a multiple of 18, then it should be completely divisible by 18. – 3 6
7 5
7 2
1. Fill in the blanks. Here, the remainder is 3, so 435 is not completely divisible by 18. – 3
( a) _________ is a factor of every number. Hence, 435 is not a multiple of 18.

( b) The greatest factor of a number is the _________.
Fast Check Logical Thinking
( c) The number _________ has only one factor.
Match column I with column II.
( d) When a number is divided by its factor, the remainder is _________. Column I Column II
( e) The smallest number which has exactly two factors (1 and the number itself) is (a) 18 (i) multiple of 24
_________. (b) 49 (ii) greatest factor of 18

( f) The factor of a non-zero number is either _______ than or _______ to the number. (c) 1 (iii) multiple of 7
(d) 3 (iv) smallest factor of any number
( g) The factors of 6 are _____________. (e) 48 (v) factor of 12

2. Find all the factors of:

( a) 9 (b) 16 (c) 28 (d) 32 (e) 48 Properties of Multiples
( f) 45 (g) 72 (h) 81 (i) 100 (j) 144 1. Every number is a multiple of itself.

3. Is 9 a factor of 1004? examples: 2 = 2 × 1, 8 = 8 × 1, 24 = 24 × 1, etc.
4. Check whether the smaller number in each pair is a factor of the bigger number. 2. Every number is a multiple of 1.

( a) 8, 148 (b) 16, 296 (c) 24, 342 (d) 21, 441 examples: 5 = 5 × 1, 15 = 15 × 1, 100 = 100 × 1, etc.

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