A $$3$$-digit number 'cba' is divisible by $$9$$ if _____ .

$$a+b+c$$ is divisible by $$9$$

$$a+2b+c$$ is divisible by $$9$$

$$2a+b+c$$ is divisible by $$9$$

$$a+b+2c$$ is divisible by $$9$$

MCQ Questions for Class 6 Maths Playing With Numbers Quiz 9

Find the number divisible by

$3$ .

0%
$602$
0%
$563$
0%
$991$
0%
$753$

Explanation

We know the divisibility rule for

$3$ :
If the sum of the digits of a number is divisible by

$3$ , then the number is also divisible by

$3$ .
Here,

$7 + 5 + 3 = 15$ is divisible by

$3$ .

So, option D is correct.

How many of the prime factors of

$30$ are greater than

$2$ ?

0%
One
0%
Two
0%
Three
0%
Four
0%
Five

Explanation

$30=2\times 3\times 5$
So, only

$3$ and

$5$ are the two prime factors that are greater than

$2$ .

What is the largest

$3$ digit number exactly divisible by

$3$ ?

0%
$972$
0%
$990$
0%
$996$
0%
$993$

Explanation

We know the divisibility rule for

$3$ :
If the sum of the digits of a number is divisible by

$3$ , then the number is also divisible by

$3$ .
Here,

$9 + 9 + 6 = 24$ is multiple of

$3$ .
So,

$996$ is the largest number divisible by

$3$ .

So, option C is correct.

Which number is divisible by

$9$ ?

0%
$863$
0%
$932$
0%
$752$
0%
$837$

Explanation

${\textbf{Step -1: Sum of digits of 863 = 17}}$

${\text{17 is not divisble by 9}}$

${\textbf{Step -2: Sum of digits of 932 = 14}}$

${\text{14 is not divisible by 9}}$

${\textbf{Step -3:Sum of digits of 752 = 14}}$

${\text{14 is not divisible by 9}}$

${\textbf{Step -4: Sum of digits of 837 = 18}}$

${\text{18 is divisible by 9}}$

${\textbf{Hence, 837 is divisible by 9 .}}$

What is the number that should be added to

$27549$ to make it exactly divisible by

$3$ ?

0%
$0$
0%
$2$
0%
$4$
0%
$5$

Explanation

If sum of digits of a number is divisible by

$3$ then that number is also divisible by

$3$ .

Here,

$2 + 7 + 5 + 4 + 9 = 27$ , which is a multiple of

$3$ .
Hence, no addition is required to make this number to be divisible by

$3$ .

So, option A is correct.

Find the number of prime numbers between 301 and 320?

0%
6
0%
5
0%
4
0%
3

Explanation

Prime numbers between 301 and 320 are 307, 311, 313, 317. So there are total $4$ prime numbers between 301 and 320

So correct answer will be option C

Every composite number has _____________.

0%
no prime divisor
0%
one and only one prime divisor
0%
atleast one prime divisor
0%
atleast two prime divisor

Explanation

A composite number is that has at least one prime divisor other than

$1$ and itself. For example :

$10$ is composite number that has

$2, 5$ as its prime divisors.

Find all of the factors of

$47$ .

0%
1
0%
17
0%
23
0%
47

Explanation

$47$ is a prime number.
So, the divisors of

$47$ is

$1,47$ .

What is the largest odd number that is a factor of

$860$ ?

0%
$143$
0%
$115$
0%
$215$
0%
$243$

Explanation

Factorisation of

$860=$

$2\times 430=2\times 2\times 215$

$215$ is an odd number, so the largest odd number factor of

$860$ is

$215$ .

What smallest number should be added to 4456 so that the sum is completely divisible by 6?

0%
$4$
0%
$3$
0%
$2$
0%
$1$
0%
None of these

Explanation

We know that the divisibility test of

$6$ states that a number is divisible by

$6$ if the number is even and the sum of the digits is divisible by

$3$ .

Since,

$4456\div 6$ (Quotient

$=742,$ Remainder

$=4$ )

Therefore required number

$=(6-4)=2$

Hence,

$2$ is the smallest number that should be added to

$4456$ so that the sum is completely divisible by

$6$ .

Find

$HCF$ by finding factors :

$75, 79$ and

$89$

0%
$2$
0%
$3$
0%
$1$
0%
$4$

Explanation

Factorization of the following

$75 = 5 \times 5 \times 3\times 1$

$79=1 \times 79$

$89 = 1 \times 89$

Since, the common factor is

$1$ this implies that

$HCF = 1$

Hence, the correct option is

$C$

Find

$HCF$ by finding factors:

$6$ and

$8$ .

0%
$4$
0%
$6$
0%
$2$
0%
$8$

Explanation

Factorization of the following.

$6 = 3 \times 2\times 1$

$8 = 2 \times 2 \times 8\times 1$

Since, The common factor is

$2$ .This implies that

$H.C.F = 2$

Hence,the correct option is

$C$

$3$ -digit number 'cba' is divisible by

$9$ if _____ .

0%
$a+2b+c$ is divisible by $9$
0%
$2a+b+c$ is divisible by $9$
0%
$a+b+2c$ is divisible by $9$
0%
$a+b+c$ is divisible by $9$

Explanation

Divisibility Test for

$9$ :

$\rightarrow$ A number is divisible by

$9$ if the sum of the digits is divisible by

$9$ .

For Example,

$549$ is divisible by

$9$ since the sum of the digits is

$18$ and

$18$ is Divisible by

$9$ .

Here,

Given number is 'cba'

For it to be Divisible by

$9$ ,

(a+b+c) should be divisible by

$9$

$\therefore$ Answer is 'D'

How many one digit numbers are divisible by

$2$

0%
$1$
0%
$4$
0%
$5$
0%
$6$

Explanation

We know the divisibility rule for

$2$ :
Always check the last digit end with

$0, 2, 4, 6$ or

$8$ .
So one digit numbers which are divisible by

$2$ are

$0, 2, 4, 6, 8$ .

Sum of factors of

$78$ are ________.

0%
$168$
0%
$170$
0%
$167$
0%
$189$

Explanation

Factors of

$78$ are

$1, 2, 3, 6, 13, 26, 39$ and

$78$ .

Required sum

$= 1 + 2 + 3 + 6 + 13 + 26 + 39 + 78$

$= 168$ .

The number which have only two factors

$(1$ and the number itself) are called as ________.

0%
Composite
0%
Even
0%
Prime
0%
None of these

Which of the following pair of numbers is co-prime?

0%
$(17, 15)$
0%
$(10, 16)$
0%
$(20, 24)$
0%
$(31, 62)$

Explanation

In number theory, Co-prime numbers are those numbers if the only positive factor that divides them is

$1$ .

Here,

Option A:

$(17,15)$ Factor that divides both of them is

$1$ .

Option B:

$(10,16)$ Factors that divides both oh them are

$1,2.$

Option C:

$(20,24)$ Factors that divide both of them are

$1,2,4.$

Option C:

$(31,62)$ Factors that divide both oh them are

$1,31.$

In reference to above definition

$(17,15)$ are co-prime numbers.

Hence Option A is correct.

Choose the correct answers from the alternatives given.

$9^6$ - 11 when divided by 8 would leave a remainder of _______________.

0%
0
0%
6
0%
2
0%
3

Which of the following is a pair of co-primes?

0%
$(14, 35)$
0%
$(18, 25)$
0%
$(31,93)$
0%
$(32, 62)$

Explanation

If the H.C.F of two numbers are

$1$ they are said to be co-prime

Factors of

$14=1,2,7$

Factors of

$35=1,5,7$

$\Rightarrow$ Common factor

$=1,7$

$\therefore$

$(14,35)$ is not pair of co-prime.

Factors of

$18=1,2,3,6,9$

Factors of

$25=1,5$

$\Rightarrow$ Common factor

$=1$

$\therefore$

$(18,25)$ is pair of co-prime.

Factors of

$31=1,31$

Factors of

$93=1,3,31$

$\Rightarrow$ Common factor

$=1,31$

$\therefore$

$(31,93)$ is not pair of co-prime.

Factors of

$32=1,2,4,8,16$

Factors of

$62=1,2,31$

$\Rightarrow$ Common factor

$=1,2$

$\therefore$

$(32,62)$ is not pair of co-prime.

Which of the following is perfect number ?

0%
$6$
0%
$7$
0%
$8$
0%
$9$

Explanation

A number is called a perfect number if by adding all the positive divisors of the number (except itself), the result is the number itself.

$(a)6$ is the first perfect number. Its divisors (other than the number itself:

$6$ ) are

$1, 2,$ and

$3$ and

$1 + 2 + 3=6$ .

$(b)7$ is the not a perfect number. Its divisors (other than the number itself:

$7$ ) are

$1$ and

$1\neq\,7$ .

$(c)8$ is the not a perfect number. Its divisors (other than the number itself:

$8$ ) are

$1,2$ and

$4$ and

$1+2+4=7\neq 8$ .

$(d)9$ is the not a perfect number. Its divisors (other than the number itself:

$9$ ) are

$1$ and

$3$ and

$1+3=4\neq9$ .

The number of prime numbers between

$1 \ and \ 10$ is

0%
$12$
0%
$4$
0%
$3$
0%
$2$

Explanation

The prime numbers between

$1$ to

$10$ is,

$2,3,5,7,$

There are four prime numbers in between

$1$ to

$10$ .

Find the HCF of

$25$ and

$30$ .

0%
$25$
0%
$6$
0%
$1$
0%
$5$

Explanation

$\Rightarrow$ $25=5\times5$

$\Rightarrow$ $30=5\times6$

Hence the Highest common factor is 5

Therefore HCF is $5$

Choose the composite numbers from the following numbers

$87, 67, 45, 34, 23, 27, 33$ .

0%
$45, 87, 34, 27, 33$
0%
$45, 87, 67, 33$
0%
$33, 27, 23, 34$
0%
All the above
0%
None of these

Explanation

$87, 45, 34, 33, 27$ are composite numbers

[A composite number define as except own and one which are divisible by any numbers such that (4,6,8,9,....)]

Which of the following numbers is divisible by

$3$ ?

0%
$561$
0%
$467$
0%
$233$
0%
None of these

Factor of 30 are :

0%
2,3,5
0%
1,2,3,5,16
0%
1,2,3,10,15
0%
1,2,3,5,6

Find the factors of

$15$ using multiplication.

0%
$1,3,5,7,15$
0%
$1,2,3,5,15$
0%
$1,5,7,15$
0%
$1,3,5,15$

Which of the pairs are co-primes ?

0%
$15$ and $33$
0%
$24$ and $29$
0%
$17$ and $19$
0%
All of above

Explanation

If the H.C.F of two numbers are

$1$ they are said to be co-prime.

In all the cases, we have only one common factor and that is 1.

Hence answer is D.

How many prime numbers are there in the following series.

$1,2,7,9,13,15,21,23,27,29$

0%
7
0%
6
0%
5
0%
4

Which of the following is a prime number

0%
391
0%
899
0%
621
0%
199

The factor of 45 is

0%
10
0%
4
0%
5
0%
6

Explanation

$45 = 3 \times 3 \times 5$ .

CBSE Questions for Class 6 Maths Playing With Numbers Quiz 9 - MCQExams.com

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Practice Class 6 Maths Quiz Questions and Answers

CBSE Questions for Class 6 Maths Playing With Numbers Quiz 9 - MCQExams.com

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Practice Class 6 Maths Quiz Questions and Answers

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