Worksheet 5
me following questions. First one is done for you.
(a) Is 5 a factor of 36? (No: 36 + 5 = 7 and remainder = 1)
(b) Is 7 a factor of 77?
(c) Is 8 a factor of 62?
(d) is 9 a factor of 70?
(1)
Is 15 a factor of 100?
(g) Is 20 a factor of 140?
(e) Is 12 a factor of 120?
(h) Is 6 a factor of 284?
2. Fill in the blanks.
(a) 2 x 7 = 14 : 2 and
are the factors of 14.
(b) 3 x 8 = 24 :
8
and 8 are the factors of 24.
(c) 5 x 7 = 35 : 5 and 7 are the factors of
(d)
4 x 5 = 20 : 4 and 5 are the
of 20.
_ of 56.
(e) 7 x 8 = 56 : 7 and
are the _
3. Write all the factors of the following numbers.
(a) 12 (c) 28 (1) 45 (9) 50
(b) 32 (1) 35 (1) 60 (h) 72
(1) 96
( 84
(k) 88
(1) 71
COMMON FACTORS
1. Taking two numbers.
Let us take two numbers say, 8 and 12.
Factors of 8 : 1, 2, 4, 8
Factors of 12 : 0, 2), 3, 4, 6, 12
So, the common factors of 8 and 12 are 1, 2 and 4.
Answers
Answer:
I don't know the answer
Step-by-step explanation:
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Answer:
(i)

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15 is not completely divisible by 2
i.e., 14 ÷ 2 = 7 or dividend ÷ divisor = quotient
When a number (dividend) is completely divided by another number (divisor), then this divisor is called a factor and the dividend is called a multiple of the divisor.
Here 2 is the factor of the multiple 14.
14 ÷ 1 = 14, 14 ÷ 14 = 1, 14÷ 7 = 2
So the divisors 1, 14 and 7 are also the complete divisors or factors of the dividend (multiple) 14.
Thus, the factor must be a complete divisor of the multiple (dividend).
(ii) 18 ÷ 2 = 9,
18 ÷ 3 = 6,
18 ÷ 9 = 2,
18÷ 6 = 3,
18 ÷ 1 = 18,
18 ÷ 18 = 1
If 18 are divided by 2, 3, 9, 6, 1 and 18, it is completely divided.
Thus, 2, 3, 9, 6, 1, 18 or 1, 2, 3, 6, 9 and 18 are the complete divisors or the factors of the multiple 18.
We may define a factor as the multiplier or complete divisor of its multiple.
A multiple has many but limited numbers of factors.
35 have 4 factors, i.e., 1, 5, 7 and 35.
42 have 8 factors, i.e., 1, 2, 3, 6, 7, 14, 21 and 42.
(iii) Let us find the factors of 24.
By division method
24 ÷ 1 = 24
24 ÷ 2 = 12
24 ÷ 3 = 8
24 ÷ 4 = 6
1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24
Taking help of division to check multiples
(i) Is 24 a multiple of 8? Use division.
24 ÷ 8 = 3 (No remainder)
Yes, 24 is a multiple of 8.
(ii) Is 56 a multiple of 5? Use division.
56 ÷ 5

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Here remainder is 1
56 is not a multiple of 5 because there is a remainder.
(iii) Is 456 a multiple of 9? Use division.
456 ÷ 9

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Here remainder is 6
456 is not a multiple of 9 because there is a remainder.
Note:
In division if there is no remainder, the dividend is the multiple of the divisor.
Finding the factors of a number through division
(i) Take a look. Is 5 a factor of 15?
15 ÷ 5 = 3 15 ÷ 3 = 5

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No remainder No remainder
5 is factor of 15. 3 is a factor of 15.
Both 3 and 5 are factor of 15.
(ii) Find the factors of 36:

1 × 36 = 36 2 × 18 = 36 3 × 12 = 36

4 × 9 = 36 5 is not a factor of 36 6 × 6 = 36
Note:
No need to do any more division because the factors are getting repeated.
Now we can write the factors like this:
The factors of 36 are:
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Note:
It is very important to work systematically in math.
(iii) Is 7 a factor of 24?
24 ÷ 7 = 3 remainder 3

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Here, remainder = 3
7 is not a factor of 24.
Taking help of division to check multiples
(i) Is 24 a multiple of 8? Use division.
24 ÷ 8 = 3 (No remainder)
Yes, 24 is a multiple of 8.
(ii) Is 56 a multiple of 5? Use division.
56 ÷ 5

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Here remainder is 1
56 is not a multiple of 5 because there is a remainder.
(iii) Is 456 a multiple of 9? Use division.
456 ÷ 9

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Here remainder is 6
456 is not a multiple of 9 because there is a remainder.