Be My Multiple, I'll be Your Factor Test 2

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Be My Multiple, I'll be Your Factor Test 2

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Question 1
1 / -0

the first four common multiple of numbers $$6,8,10$$ are

A
$$10,20,30,40$$

B
$$120,240,360,480$$

C
$$8,40,80,120$$

D
$$6,60,120,240$$

Solution

$$6 = 2\times3$$
$$8 = 2^{3}$$
$$10 = 2\times5$$

$$\Rightarrow$$ LCM of $$6,8,10 = 2^{3}\times3\times5 = 120$$

$$\therefore 120$$ is the least common multiple of $$6,8,10$$. Thus, all multiples of $$120$$ are common multiples of $$6,8$$ and $$10$$.

$$\therefore$$ First four common multiples $$= 120,240,360,480$$
Question 2
1 / -0

Find two common multiples of $$12,15$$

A
$$48,96$$

B
$$60,120$$

C
$$10,20$$

D
$$24,30$$

Solution

Multiples of 12 are 12,24,36,48,60,72,84,96,108,120
Multiples of 15 are 15,30,45,60,75,90,105,120
Answer $$= 60,120$$
Question 3
1 / -0

The 1st two common multiple of numbers $$12,8,16 $$ are:

A
$$12,24$$

B
$$8,16$$

C
$$16,32$$

D
$$48,96$$

Solution

Multiples of $$12$$ are $$12,24,36,48,60,72,84,96,108,120....$$
Multiples of $$8$$ are $$8,16,24,32,40,48,56,64,72,80,88,96......$$.
Multiples of $$16$$ are $$16,32,48,64,80,96........$$

$$\therefore$$ First two common multiples $$= 48,96$$
Question 4
1 / -0

Which of the following is greatest?

A
$$4$$th multiple of $$52$$

B
$$8$$th multiple of $$37$$

C
$$5$$th multiple of $$25$$

D
$$7$$th multiple of $$50$$

Solution

(a) $$4$$th multiple of $$52=52\times 4=208$$
(b) $$8$$th multiple of $$37=37\times 8=296$$
(c) $$5$$th multiple of $$25=25\times 5=125$$
(d) $$7$$th multiple of $$50=50\times 7=350$$
So, $$350$$ is the greatest value amongst all.
Question 5
1 / -0

Find the 1st common multiple of $$6$$ and $$8$$.

A
$$24$$

B
$$16$$

C
$$12$$

D
$$2$$

Solution

Multiples of 6 are 6,12,18,24,30,36,42....
Multiples of 8 are 8,16,24,32,40,48......
So,first common multiple of 6 and 8 is 24
Question 6
1 / -0

$$x$$ is twice the difference between the $$6$$th and $$10$$th multiple of $$7$$. Find the value of $$x$$.

A
$$38$$

B
$$56$$

C
$$60$$

D
$$28$$

Solution

$$6$$th multiple of $$7=42$$
$$10$$th multiple of $$7=70$$
Now, $$x=2\times (70-42)=2\times 28=56$$
Question 7
1 / -0

What are the common factors of numbers $$10$$ and $$12$$?

A
1,2,3,5

B
1,4,6

C
1,2,5,8

D
1,2

Solution

Factors of $$ 10 $$ are $$ 1, 2, 5,10 $$
Factors of $$ 12 $$ are $$ 1, 2, 3,4, 6, 12, $$
$$\therefore $$ common factors are $$ 1, 2$$.
Question 8
1 / -0

Find all the prime factors of 24 and 36 and hence find the Highest Common Factor all 24 and 36.

A
2

B
4

C
12

D
8

Solution

$$24=2\times2\times2\times3$$
$$36=2\times2\times3\times3$$
highest common factor is $$2\times2\times3=12$$
Question 9
1 / -0

find Highest Common factor of 5 and 6.

A
5

B
1

C
6

D
None of the above

Solution

$$5=1\times5$$
$$6=1\times2\times3$$
HCF is 1
Question 10
1 / -0

What do you mean by co-prime numbers. Explain with examples.

A
Numbers having any two factors in common

B
Numbers having more than two factors in common

C
Numbers having two factors in common- 1 and the number itself

D
Numbers having one factor in common i.e. 1

Solution

Co-prime numbers are set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1.

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Be My Multiple, I'll be Your Factor Test 2

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Be My Multiple, I'll be Your Factor Test 2

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SHARING IS CARING

Question 1

$$10,20,30,40$$

$$120,240,360,480$$

$$8,40,80,120$$

$$6,60,120,240$$

Solution

Question 2

$$48,96$$

$$60,120$$

$$10,20$$

$$24,30$$

Solution

Question 3

$$12,24$$

$$8,16$$

$$16,32$$

$$48,96$$

Solution

Question 4

$$4$$th multiple of $$52$$

$$8$$th multiple of $$37$$

$$5$$th multiple of $$25$$

$$7$$th multiple of $$50$$

Solution

Question 5

$$24$$

$$16$$

$$12$$

$$2$$

Solution

Question 6

$$38$$

$$56$$

$$60$$

$$28$$

Solution

Question 7

1,2,3,5

1,4,6

1,2,5,8

1,2

Solution

Question 8

2

4

12

8

Solution

Question 9

5

1

6

None of the above

Solution

Question 10

Numbers having any two factors in common

Numbers having more than two factors in common

Numbers having two factors in common- 1 and the number itself

Numbers having one factor in common i.e. 1

Solution

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