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

Mind Map Creative Thinking
math

Factors FACtorS ANd MULtIPLeS Multiples

Factors of a given number The multiples of a number
are the numbers which Prime Factorisation are obtained by multiplying it
divide the given number It is the process of expressing a number with the numbers 1, 2, 3, 4
exactly. as a product of prime factors. and so on.
E.g.: the factors of 30 are E.g.: the multiples of 12 are
1, 2, 3, 5, 6, 10, 15 and 12 × 1 = 12, 12 × 2 = 24, 12
30. Factor tree Method division Method × 3 = 36, 12 × 4 = 48, …
36 2 60
Highest Common Factor 18 2 30
(HCF) 2 × 3 15 Least Common Multiples (LCM)
5 5
The largest common 2 × 9 1 The smallest number among
factor is called the highest 3 × 3 the common multiples is
common factor or HCF. Prime factorisation of 36 Prime factorisation of 60 called the least common
is 2 × 2 × 3 × 3 is 2 × 2 × 3 × 5 multiple or LCM.
Common Factors Method divisibility rule 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
E.g., HCF of 12 and 30.
A number
Factors of 12 = 1, 2, 3, 4, is divisible divisiblity rule examples Methods of Finding the LCM
6 and 12 by Common multiple method
Factors of 30 = 1, 2, 3, 5, if the digit in its ones 424, 1024, etc. are E.g., LCM of 15 and 20.
6, 10, 15 and 30. 2 place is 0, 2, 4, 6 or 8. divisible by 2. Multiples of 15 = 15, 30, 45,
Common factors of 12 and if the sum of the 1863 is divisible by 3. 60, 75, 90, ...
30 = 1, 2, 3 and 6. 3 digits of the number is Multiples of 20 = 20, 40, 60,
Highest common factor divisible by 3. 80, ...
(HCF) of 12 and 30 is 6. if the number formed 428 is divisible by 4. Common multiples of 15 and
by the last two digits 20 = 60, 120, ...
Least common multiple (LCM)
Prime Factorisation Method 4 (tens and ones digits) of of 15 and 20 = 60.
E.g., HCF of 60 and 80. the number is divisible
Prime factors by 4.
of 60 of 80 5 if the digit in its ones 275, 400, 5225 etc. Prime Factorisation Method
2 60 2 80 place is either 0 or 5. are divisible by 5. E.g., LCM of 64, 48 and 320.
2 30 2 40 if the number is 3144 is divisible by 2 64 2 48 2 320
3 15 2 20 6 divisible by both 2 and 6 as it is divisible 2 2 32 2 24 2 160
5 2 10 2 16 2 12 2 80
5 3. and 3. 2 8 2 6 2 40
3
2 20
60 = 2 × 2 × 3 × 5 if the number formed 2592 is divisible by 8. 2 4 2 10
by the last three digits 2 5
80 = 2 × 2 × 2 × 2 × 5 8 (hundreds, tens and 64 = 2 × 2 × 2 × 2 × 2 × 2
HCF of 60 and 80 = 2 × 2 ones digits) of the 48 = 2 × 2 × 2 × 2 × 3
× 5 = 20. number is divisible by 8. 320 = 2 × 2 × 2 × 2 × 2 × 2 × 5
if the sum of the 1692 is divisible by 9. LCM of 64, 48 and 320 is 2 × 2
Long division Method 9 digits of the number is × 2 × 2 × 2 × 2 × 3 × 5 = 960.
E.g., HCF of 492 and 124 divisible by 9.
124 492 3 10 if the digit in the ones 1050, 3000 and 5500
– 372 place is 0. are divisible by 10. division Method
120 124 1 if the difference of the 25861 is divisible by E.g., LCM of 12, 16 and 20.
– 120 2 12,16, 20
4 120 30 sum of digits at odd 11. 2 6, 8, 10
– 12 places and the sum of 2 3, 4, 5
00 11 digits at even places is
– 00 3, 2, 5
0 either 0 or divisible by LCM of 12, 16 and 20 = 2 × 2
HCF of 492 and 124 = 4. 11. × 2 × 3 × 2 × 5 = 240.

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