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