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\\January 6, 2024 3:29 PM Bharat Arora Proof-3 Reader _________________________ Date: ___________________74

Encapsulate
math
Factors and multiples

Factors multiples test of divisibility

A factor is a number that A multiple is the product � 2 The last digit is even.
divides a given number of two or more factors. � 3 The sum of the digits is divisible by 3.
without leaving a remainder. example: � 4 Number formed by last two digits is divisible
by 4 or the last two digits are 00.
example: � 5 The last digit is either 0 or 5.
4 × 1 = 4
45 ÷ 1 = 45 4 × 2 = 8 � 6 Divisible by both 2 and 3.
45 ÷ 3 = 15 4 × 3 = 12 � 9 The sum of the digits is divisible by 9.
The number ends in 0.
� 10
45 ÷ 5 = 9 4 × 4 = 16
45 ÷ 9 = 5 4 × 5 = 20 prime and composite numbers
45 ÷ 15 = 3 4 × 6 = 24 � Prime numbers: Have only two factors—1 and itself.
45 ÷ 45 = 1 Example: 2, 5, 7, ...
Multiples of 4 are 4, 8, 12, � Composite number: Have more than two factors.
Factors of 45 are 1, 3, 5, 9, Example: 4, 6, 8, ...
15, and 45. 16, 20, ... � 1 is neither prime nor composite.

common Factors prime Factorisation
Factors of 18 are: Factor tree method division method
1 , 2, 3 , 6, 9 , 18
Factors of 27 are: example: or
1 , 3 , 9 , 27 24 24 2 24
Common Factors: 2 12
1, 3 and 9 2 6
4 × 6 2 × 12
common multiples 3

Multiples of 8 are Prime factorisation of
8, 16, 24 , 32, 40, 48 ,... 2 × 2 2 × 3 2 × 6 24 = 2 × 2 × 2 × 3
Multiples of 12 are:
Multiples of 12:
12, 24 , 36, 48 , 60,... Prime factorisation of
24 = 2 × 2 × 2 × 3
Common multiples: 24, 48
Common multiples: 24, 48,... 2 × 3

Brain Sizzlers

Iqra set a 4-digit number as the passcode on her mother’s
mobile such that the passcode is divisible by 9. She did not use
the phone for a long time. She forgot the passcode when she
wanted to unlock it. Out of four digits, she remembered only

first three digits, which are 2, 4 and 1. What is the passcode?

106 Mathematics-4