 # FACTORS AND MULTIPLES

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Factors

A factor (divisor) of a number is a number that can divide it evenly (that is, without a remainder). For example, the factors of 24 are 1, 2, 3, 4, 6, 12 and 24.  A common factor of x and y is a number that is a factor of x and also of y. For example, 6 is a common factor of 24 and 39. A prime factor is a factor that is also a prime number. For example, the prime factor of 24 are 2 and 3. When the word “divisible” appears in a question, it means “evenly divisible” or “divisible without a remainder.”

 Number Factor 1 1 2 1, 2 3 1, 3 4 1, 2, 4 5 1, 5 6 1, 2, 3, 6 7 1, 7 8 1, 2, 4, 8 9 1, 3, 9 10 1, 2, 5, 10 11 1, 11 12 1, 2, 3, 4, 6, 12 13 1, 13 14 1, 2, 7, 14 15 1, 3, 5, 15 16 1, 2, 4, 8, 16 17 1, 17 18 1, 2, 3, 6, 9, 18 19 1, 19 20 1, 2, 4, 5,10,20 21 1, 3, 7, 21 22 1, 2, 11, 22 23 1, 23 24 1, 2, 3, 4, 6, 8, 12, 24 25 1, 5, 25

Note: The only number that has one factor is one (1)

MULTIPLE

A multiple of a number is a number that is evenly divisible by it. For example, 16, 32, and 88 are multiples of 8.

14, 21, 28 are multiple of 7

E.g: what are the first 3 multiple of 2, 4, 6, 10 and 12?

2 = 2, 4, 6

4 = 4, 8, 12

6 = 6, 12, 18

10 = 10, 20, 30

12 = 12, 24, 36

LOWEST COMMON MULTIPLES (L.C.M) AND HIGHEST COMMON FACTOR (H.C.F)

Lowest Common Multiple (L.C.M)

This means the smallest possible number that can be divided by a particular set of numbers

e.g. 1:   Find the l.c.m of 4, 6 and 8

Set of numbers are 4,  6 and 8

2       4          6          8

2       2          3          4

2       1          3          2

3       1          3          1

s        1          1          1

2×2×2×3=24

Lcm= 24

e.g. 2: Find the LCM of 15, 18 and 24

2       15        18        24

2       15        9          12

2       15        9          6

3       15        9          3

3       5          3          1

5       5          1          1

1          1          1

2×2×2×2×3×3×5=360

LCM= 360

e.g. 3: Find the LCM of 7, 14 and 21

2       7          14        28

2       7          7          14

7       7          7          7

1          1          1

2×2×2×7=56

Lcm= 56

e.g 4: Find the lcm of 24, 36, and 48

2       24        36        48

2       12        18        24

2       6          9          12

2       3          9          6

3       3          9          3

3       1          3          1

1          1          1

2×2×2×2×3×3=144

LCM= 144

Highest Common Factor (H.C.F)

This means the highest possible factor or number that can be divided by a set of number without   remainder.

e.g. 1: What is the h.c.f of 6, 12 and 15?

3       6          12        15

2          4          5

Hcf= 3

e.g. 2: What is the hcf of 12, 16vand 24

2       12        16        24

2       6          8          12

3          4          6

Hcf= 2×2=4

OR

State the factors and pick the highest common factor

12= 1, 2, 3, 4, 6, 12

16= 1, 2, 4, 8, 16

24= 1, 2, 3, 4, 6, 8, 12, 24

Common factors (cf) = 1, 2, 4

Hcf= 4

e.g. 3: Find the hcf of 12, 13 and 15

12= 1, 2, 3, 4, 6, 12

13= 1, 13

15= 1, 3, 5, 15

Cf= 1

Hcf=   1

e.g. 4: Find the difference between the LCM and HCF of 8, 12 and 24

2     8     12     24                                                           8= 1, 2, 4, 8

2     4      6      12                                                             12=1, 2, 3, 4, 6, 12

2      2      3       6                                                             24=1, 2, 3, 4, 6, 8, 12, 24

3      1      3       3                                                                         Cf=1, 2, 4

1      1       1                                                                         Hcf=4

2×2×2×3= 24

LCM=24

LCM-HCF

24 – 4= 20

e.g. 5: Find the difference between the lcm and hcf of 18, 24 and 36

2      18     24     36                                  18=1, 2, 3, 6, 9, 18

2       9      12     18                                  24=1, 2, 3, 4, 6, 8, 12, 24

2       9       6       9                                    36= 1, 2, 3, 4, 6, 12, 18, 36

3       9       3       9                                                cf= 1, 2, 3, 6

3       3       1       3                                                     Hcf= 6

1       1       1

2×2×2×3×3=72

LCM= 72

LCM-HCF

72-6= 66

Quiz

1. Write out the factors of 64
2. Find the LCM of 8, 12 and 16.
3. What is the HCF of 8, 12 and 16?
4. Find the difference between the LCM and HCF of 6, 12 and 18
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