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PRIME TIME

Multiples Factors Prime Factorisation
The multiples of a number are Factors of a given number are the It is the process of expressing a
obtained by multiplying it with the numbers which divide the given number as a product of its prime
numbers 1, 2, 3, 4 and so on. number exactly. factors.
E.g. the multiples of 12 are: E.g., factors of 56 are 1, 2, 4, 7, 8,
12 × 1 = 12, 12 × 2 = 24, 12 × 3 = 36, 14, 28 and 56.
12 × 4 = 48.
Common Factors Factor Tree Method Division Method
Common Multiples Factors that are 60 2 60
Multiples that are common. common. Factors of 2 30 2 30
Multiples of 2: 2, 4, 6, 8, 10, 18: 1,2, 3, 6, 9 and 18. 3 15
12, ... Factors of 42 = 1, 2, 2 15
Multiples of 3: 3, 6, 9, 12, 3, 6, 7,14, 21 and 42. 5 5
15, ... Common factors of 18 2 3 1
Common multiples: 6, 12, ... and 42 are 1, 2, 3, 6. 60 = 2 × 2 × 3 × 5 60 = 2 × 2 × 3 × 5

Least Common Multiples Highest Common Factors (HCF) Co-Prime
(LCM) The largest common factor is called the Two number are co-
The smallest number among highest common factor or HCF. prime if there is no
the common multiples is other factor except 1
called the lowest common is common between
multiple or LCM. them e.g., (13, 14) (28,
Common Factors Method
Find the HCF of 36, 60. 57), etc.
Common Multiples Method Factors of 36 are 1, 2, 3, 4, 6, 9,
Find the LCM of 12 and 18. 12, 18 and 36. Divisibility Rule
Multiples of 12 are 12, 24, 36, Factors of 60 are 1, 2, 3, 4, 5, 6,
48, ... 10, 12, 15, 20, 30 and 60. Divisor Divisible Rules
Multiples of 18 are 18, 36, 54, Common factors are 1, 2, 3, 4, 6 2 If the digit at its ones place is 0, 2,
4, 6 or 8. E.g., 2346, 4680, etc.
72, ... and 12. 12 is the greatest. Hence, If the sum of the digits of a
Common multiples of 12 and the HCF of 36 and 60 is 12. 3 number is divisible by 3. E.g.,
18 are 36, 72, 108, ... So, the Prime Factorisation Method 234561
LCM of 12 and 18 is 36. Find the HCF of 70, 105 and 175. If the number formed by last
Prime Factorisation Method 4 two digits (tens and ones digit)
Find the LCM of 20, 25, 30. 2 70 3 105 5 175 of the number is divisible by 4.
2 20 5 25 2 30 5 35 3 35 5 35 E.g., 87632
If the digit at its ones place is
2 10 5 3 15 7 7 7 5 either 0 or 5. E.g., 127, 620, etc.
5 5 Thus, HCF of 70, 105 and 175 is If the difference of twice the last
LCM of 20, 25 and 30 = 2 × 2 × 5 × 7 = 35. 7 digit of the number from the
remaining number is divisible by
3 × 5 × 5 = 300. Long Division Method 7. E.g., 1561
Division Method Find the HCF of 91 and 112. If the number formed by last
Find the LCM of 8, 15 and 24. 9 112 1 8 three digits of the number is
2 8, 15, 24 – 91 divisible by 8. E.g. 45,6000
2 4, 15, 12 Last divisor 21 91 4 9 If the sum of the digits of a
number is divisible by 9. E.g., 234
2 2, 15, 6 – 84 10 If the digit at the ones place is 0.
3 1, 15, 3 7 21 3
1, 5, 1 – 21 11 If the difference of sum of digits
at odd places and sum of digits at
The LCM of 8, 15, 24 = 2 × 2 × 0 even places is 0 or divisible by 11.
2 × 3 × 5 = 120. Thus, the HCF of 91 and 112 is 7.

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