Unit-1: Factors and Multiples
EXERCISE 1.1
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1. Identify the numbers that have 18 as a factor:
54, 126, 198, 240, 320
Hint: Factor of a number are the numbers that it can be divided exactly by:
Hint: Check for all the above numbers if divisible by 18 will be the number having 18 as a factor of :
Solution:
Checking one by one that the number are completely divisible by 18 or not.
54 ÷ 18 = 3 and remainder 0 (ie. Completely divisible), so 18 is a factor of 54
126 ÷ 18 = 7 and remainder 0 (ie. Completely divisible), so 18 is a factor of 126
198 ÷ 18 = 11 and remainder 0 (ie. Completely divisible), so 18 is a factor of 198
240 ÷ 18 = 13 and remainder 6 (ie. Not Completely divisible), so 18 is not a factor of 54
Among the given numbers, 54, 126, 198 are divisible exactly by 18, so 18 is Nota factor of 54
54, 126, 198 -------------Ans.
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2. Identify the numbers below which are factors of 144.
1, 2, 3, 4, 8, 9, 12, 14, 16, 32, 48, 144
Hint: Factor of a number are the numbers that it can be divided exactly by:
Hint: Check for all the above numbers that divide 144 exactly will be the answers as a factor of 144:
Solution:
Factors of 144 are:
144 = 1 ｘ 144
144 = 2 ｘ 72
144 = 3 ｘ 48
144 = 4 ｘ 36
144 = 6 ｘ 24
144 = 8 ｘ 18
144 = 9 ｘ 16
144 = 12 ｘ 12
All factors of 144 are = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Thus
Answer: 1, 2, 3, 4, 8, 9, 12, 16, 32, 48, 144
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3. Find all factors of:
(i) 15 (ii) 21 (iii) 32
(iv) 29 (v) 40
Solutions:
(i) 15
15 = 1 ｘ 1515 = 3 ｘ 515 = 5 ｘ 3 (repeating)
All factors of 15 are = 1, 3, 5, 15 --------Ans.(i)
(ii) 21
21 = 1 ｘ 2121 = 3 ｘ 721 = 7 ｘ 2 (repeating)
All factors of 21 are = 1, 3, 7, 21 --------Ans.(ii)
(iii) 32
32 = 1 ｘ 3232 = 2 ｘ 1632 = 4 ｘ 832 = 8 ｘ 4 (repeating)
All factors of 32 are = 1, 2, 4, 8, 16, 32 --------Ans.(iii)
(iv) 29
29 = 1 ｘ 2920 = 29 ｘ 1 (repeating)
All factors of 29 are = 1, 29 --------Ans.(iv)
(v) 40
40 = 1 ｘ 4040 = 2 ｘ 2040 = 4 ｘ 1040 = 5 ｘ 840 = 8 ｘ 5 (repeating)
All factors of 40 are = 1, 2, 4, 5, 8, 10, 20, 40 --------Ans.(v)
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4. Write down the first 4 multiples of:
(i) 5 (ii) 6 (iii) 7
(iv) 9 (v) 11 (vi) 14
Solution:
(i) The first 4 multiples of 5 are: 5, 10, 15, 20
(ii) The first 4 multiples of 6 are: 6, 12, 18, 24
(iii) The first 4 multiples of 7 are: 7, 14, 21, 28
(iv) The first 4 multiples of 9 are: 9, 18, 27, 36
(v) The first 4 multiples of 11 are: 11, 22, 33, 44
(vi) The first 4 multiples of 14 are: 14, 28, 42, 64
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5. Write down the multiples of 5 between 4 and 31
Solution:
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 ...............
Thus multiples of 5 between 4 an31 are: 5, 10, 15, 20, 25,30 ----------Ans.
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6. Identify the multiples of 8 from the following.
14, 24, 32, 54, 56, 72, 30, 64, 18, 40, 78, 96, 106, 120
Hint: Check for all the above numbers if divisible by 8 completely will be the numbers of multiples of 8:
Solution:
The highest number is 120. Therefore,
Multiples of 8 up to 120 are : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120.
Now comparing multiples of 8 with question numbers: 24, 32, 56, 72, 64, 40, 96, 120 ----------Ans.
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Shortcut links for:
1. Real Life Word Problems on Financial Mathematics, Property Tax, General Sale Tax (GST), Zakat, Ushr, Profit and Loss, Markup, Percentage, Proportion.
2. 5th class Notes: English, Social Study (S.St.), General Science (G.Sc.), Urdu (اُردو), Islamiat (اسلامیات), Mathematics
3. 6th class Notes: Mathematics (National Book Foundation, 2022 and Onwards):
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1. Real Life Word Problems on Financial Mathematics, Property Tax, General Sale Tax (GST), Zakat, Ushr, Profit and Loss, Markup, Percentage, Proportion.
2. 5th class Notes: English, Social Study (S.St.), General Science (G.Sc.), Urdu (اُردو), Islamiat (اسلامیات), Mathematics
3. 6th class Notes: Mathematics (National Book Foundation, 2022 and Onwards):
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1. Website for School and College Level Physics 2. Website for School and College Level Mathematics 3. Website for Single National Curriculum Pakistan - All Subjects Notes
© 2022-23 Academic Skills and Knowledge (ASK)
Note: Write me in the comments box below for any query and also Share this information with your class-fellows and friends.
1. Website for School and College Level Physics
2. Website for School and College Level Mathematics
3. Website for Single National Curriculum Pakistan - All Subjects Notes
© 2022-23 Academic Skills and Knowledge (ASK)
Note: Write me in the comments box below for any query and also Share this information with your class-fellows and friends.
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