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E:\Working\Orange_Education\Math_Genius_5\Open_Files\CHAP_03
\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

Properties of Factors

1. 1 is a factor of every number. Knowledge Desk
examples: 1 × 5 = 5, 1 × 8 = 8, 1 × 24 = 24, etc.

2. Every number is a factor of itself. If the sum of the factors of a
number (excluding the number
examples: 7 × 1 = 7, 9 × 1 = 9, 73 × 1 = 73, etc. itself) is equal to the number,
3. Every non-zero number (except 1) has at least two then it is called a perfect
number. The first perfect
factors. 1 has only 1 factor. number is 6 as the sum of the

4. There are a finite number of factors of any number. factors of 6 is 1+2+3=6.
example: The factors of 30 are 1, 2, 3, 5, 6, 10, 15 The next is 28 (1+2+4+7+14=28).
Can you find the next one?
and 30.
So, the factors are limited.

5. Any factor of a number is equal to or less than the given Be Aware
number. 1 is the smallest factor
example: The factors of 18 are 1, 2, 3, 6, 9 and 18. of a number.

6. Zero is not a factor of any number, whereas every number is a factor of zero.

Think Tank Critical Thinking
Is your age a factor of the sum of your parents’ age?

Practice time 3a

1. Fill in the blanks.

( a) _________ is a factor of every number.

( b) The greatest factor of a number is the _________.

( c) The number _________ has only one factor.

( d) When a number is divided by its factor, the remainder is _________.
( e) The smallest number which has exactly two factors (1 and the number itself) is
_________.

( f) The factor of a non-zero number is either _______ than or _______ to the number.

( g) The factors of 6 are _____________.

2. Find all the factors of:

( a) 9 (b) 16 (c) 28 (d) 32 (e) 48
( f) 45 (g) 72 (h) 81 (i) 100 (j) 144

3. Is 9 a factor of 1004?
4. Check whether the smaller number in each pair is a factor of the bigger number.

( a) 8, 148 (b) 16, 296 (c) 24, 342 (d) 21, 441

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