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Encapsulate
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 2 30
(HCF) 2 × 18 3 15 Least Common Multiples (LCM)
The largest common 2 × 9 5 5 The smallest number among
1
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 lowest 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 LCM
6 and 12 by Common multiple method
Factors of 30 = 1, 2, 3, 5, if the digit at 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 a 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 last two digits (tens 20 = 60, 120, ...
4 and ones digit) of the Least common multiple (LCM)
Prime Factorisation Method number is divisible of 15 and 20 = 60.
E.g., HCF of 60 and 80. by 4.
Prime factors if the digit at its ones 275, 400, 5225 etc.
of 60 of 80 5 place is either 0 or 5. are divisible by 5. Prime Factorisation Method
2 60 2 80 if the number is 3144 is divisible by 6 E.g., LCM of 64, 48 and 320.
2 30 2 40 2 64 2 48 2 320
3 15 2 20 6 divisible by both 2 as it is divisible 2 and 2 32 2 24 2 160
5 2 10 and 3. 3. 2 16 2 12 2 80
5 2 8 2 6 2 40
2 20
3
60 = 2 × 2 × 3 × 5 if the number formed 2592 is divisible by 8. 2 4 2 10
by last three digits 2 5
80 = 2 × 2 × 2 × 2 × 5 (hundreds, tens and 64 = 2 × 2 × 2 × 2 × 2 × 2
HCF of 60 and 80 = 2 × 2 8 ones digit) of the 48 = 2 × 2 × 2 × 2 × 3
× 5 = 20.
number is divisible 320 = 2 × 2 × 2 × 2 × 2 × 2 × 5
by 8. LCM of 64, 48 and 320 is 2 × 2
Long division Method if the sum of the 1692 is divisible by 9. × 2 × 2 × 2 × 2 × 3 × 5 = 960.
E.g., HCF of 492 and 124 9 digits of a number is
divisible by 9.
124 492 3
– 372 10 if the digit at the ones 1050, 3000 and 5500 division Method
120 124 1 place is 0. are divisible by 10. E.g., LCM of 12, 16 and 20.
– 120 2 12,16, 20
4 120 30 if the difference of 25861 is divisible by 2 6, 8, 10
– 12 sum of digits at odd 11. 2 3, 4, 5
00 11 places and sum of
– 00 3, 2, 5
0 digits at even places is LCM of 12, 16 and 20 = 2 × 2
HCF of 492 and 124 = 4. 0 or divisible by 11. × 2 × 3 × 2 × 5 = 240.

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