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CBSE Questions for Class 6 Maths Playing With Numbers Quiz 5 - MCQExams.com
CBSE
Class 6 Maths
Playing With Numbers
Quiz 5
What is the value of
x
for which
x
,
x
+
1
,
x
+
3
are all prime numbers?
Report Question
0%
0
0%
1
0%
2
0%
101
Explanation
Option
A
:
Substitute
x
=
0
,
x
,
x
+
1
,
x
+
3
=
0
,
1
,
3
are not prime numbers.
Option
B
:
Substitute
x
=
1
,
x
,
x
+
1
,
x
+
3
=
1
,
2
,
4
are not prime numbers.
Option
C
:
Substitute
x
=
2
,
x
,
x
+
1
,
x
+
3
=
2
,
3
,
5
which are all prime numbers.
Hence, option
C
is correct.
The smallest 3 digit prime number is:
Report Question
0%
101
0%
103
0%
109
0%
113
Explanation
The smallest 3-digit number is
100
, which is divisible by
2
.
∴
100
is not a prime number.
\sqrt{100}< 11
and
101
is not divisible by any of the prime numbers
2,3,5,7,11
.
\therefore
101
is a prime number.
Hence
101
is the smallest 3-digit prime number.
Which of the following number is a prime?
Report Question
0%
667
0%
861
0%
481
0%
331
Explanation
667
is divisible by
23
861
is divisible by
3
481
is divisible by
13
331
is divisible only by
1
and
331
.
\therefore 331
is a prime number.
Which of the following is a prime number?
Report Question
0%
33
0%
81
0%
93
0%
97
Explanation
Clearly,
97
is a prime number.
Consider the following numbers.
247
203
Which of the above number is/are prime?
Report Question
0%
1
only
0%
2
only
0%
Both
1
and
2
0%
Neither
1
nor
2
Explanation
A number which is divisible by itself and
1
are prime numbers.
1.
247 = 13\times 19
2.
203 = 7\times 79
Here both the numbers have some divisors.
So, none of the two are prime.
Which one of the following is a prime number?
Report Question
0%
184
0%
171
0%
173
0%
221
Explanation
184 = 23\times 8
Therefore, cannot be prime
171 = 19\times 9
Therefore,cannot be prime
221 = 17\times 13
Therefore, cannot be prime
Hence, by elimination we have
173
as a prime number.
Which one of the following is not a prime number?
Report Question
0%
31
0%
61
0%
71
0%
91
Explanation
91
is divisible by
7
and
13
. So, it is not a prime number.
Rest all the given numbers are prime numbers since they don't have any factors other than
1
and themselves.
Find
HCF
by finding factors:
16
and
56
.
Report Question
0%
6
0%
18
0%
8
0%
9
Explanation
The given numbers are
16
and
56
Factorizing the given numbers,
16 = 2 \times 2 \times 2 \times 2
56 = 2 \times 2 \times 2 \times 7
Since, the common factors are
2,2,2
, this implies that
H.C.F = 2 \times 2 \times 2
=8
Hence, the correct option is
Op-C
.
Find HCF of
66
and
88
.
Report Question
0%
21
0%
23
0%
24
0%
22
Explanation
Factorization of the following
66 = 1 \times 3 \times 2 \times 11
88 = 1 \times 2 \times 2 \times 2 \times 11
Since, the common factor is
1,2,11
this implies that
HCF=22
Hince, the correct option
D
Find HCF of
54, 81
and
99
.
Report Question
0%
8
0%
9
0%
10
0%
11
Explanation
Factorization of the following.
54 = 2 \times 3 \times 3 \times 3
81 = 3 \times 3 \times 3 \times 3
99 = 3 \times 3 \times 11
Since, the common factor is
3 \times 3
,this implies that
H.C.F = 3 \times 3
Hence,the correct option
B
.
HCF of two co-prime number is _______.
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0%
1
0%
0
0%
2
0%
None of these
Explanation
HCF of two co-prime numbers is
1
because they have only
1
as a common factor.
HCF of two or more prime numbers is ___________.
Report Question
0%
0
0%
2
0%
4
0%
1
Explanation
HCF of two or more prime numbers is
1
Let us take an example,
5
and
7
both are prime numbers.
5=1\times5
7=1\times7
So, HCF
=1
Hence,
Op-D
is correct.
Which of the following numbers is prime?
Report Question
0%
119
0%
187
0%
247
0%
179
Explanation
119
is divisible by
7
187
is divissible by
11
247
is divisible by
13
Bt
179
is not divisible by any number.
Hence
179
is a prime number.
( 7 \times 11 \times 13 + 13 )
is a/an
Report Question
0%
Composite number
0%
Prime number
0%
Irrational number
0%
Imaginary number.
Explanation
(7\times 11\times 13+13)=13\{(7\times11)+1\}=13\times 78=1014
Since,
1014
is divided by
13,78
which is other than
1
and the number itself, so it is a composite number.
The co-prime numbers from the following pairs, are ______.
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0%
7 and 63
0%
36 and 25
0%
35 and 29
0%
63 and 81
Explanation
If the H.C.F of two numbers are
1
they are said to be co-prime
(A) HCF (7, 63) = 7
(B) HCF (36, 25) = 1
(C) HCF (35, 29) = 1
(D) HCF (63, 81) = 9
So, 36 & 25 and 35 & 29 are co-prime numbers.
G.C.D of
4
and
19
is _________.
Report Question
0%
1
0%
4
0%
19
0%
76
Explanation
There is no common factor between
4
and
19
. Hence, G.C.D. of
4
and
19
is
1
.
The reciprocal of the smallest prime number is _______.
Report Question
0%
0
0%
\dfrac {1}{2}
0%
1
0%
2
Explanation
Prime no. are those which has only two factors.
One and the number itself.
Note:
1
is neither prime nor composite.
So, the smallest prime number is
2
.
Hence, reciprocal of
2
= \dfrac{1}{2}
Which of the following is not a prime number?
Report Question
0%
23
0%
29
0%
43
0%
21
Explanation
Factors of
23 = 23 \times 1
Factors of
29 = 29 \times 1
Factors of
43 = 43 \times 1
Factors of
21 = 3 \times 7
So, ioption D
23
is not a prime number
The number
111111111
is a
Report Question
0%
Prime number
0%
Composite number
0%
Divisible by
\frac{10^7-1}{9}
0%
None of these
Explanation
A whole number that can be divided exactly by numbers other than 1 or itself is known as composite numbers.
111111111 is an odd composite number. It is composed of three distinct prime numbers multiplied together.
Prime factorisation of
111111111 = {3}^{2} \times 37 \times 333667
Which of the following numbers are co-prime?
a)
18
and
35
b)
15
and
37
c)
30
and
415
d)
17
and
68
e)
216
and
215
f)
81
and
16
Report Question
0%
a,b and f
0%
a,b,e and f
0%
ab,c and f
0%
b,d and f
Explanation
Two numbers are co-prime, if the only positive integer that divides both of them is
1
. That is, their H.C.F.
=1
(a)
18=1\times 2\times 3\times 3
35=1\times 5\times 7
H.C.F.=1
So, the numbers are co-prime.
(b)
15=1\times 3\times 5
37=1\times 37
H.C.F.=1
So, the numbers are co-prime.
(c)
30=1\times 2\times 3\times 5
415=1\times 5\times 83
H.C.F.=5
So, the numbers are not co-prime.
(d)
17=1\times 17
68=1\times 2\times 2\times 17
H.C.F.=17
So, the numbers are not co-prime.
(e)
216=1\times 2\times 2\times 2\times 3\times 3\times 3
215=1\times 5\times 43
H.C.F.=1
So, the numbers are co-prime.
(f)
16=1\times 2\times 2\times 2\times 2
81=1\times 3\times 3\times 3\times 3
H.C.F.=1
So, the numbers are co-prime.
The total number of factors for
50
are
Report Question
0%
16
0%
6
0%
4
0%
10
Explanation
No. of factors for
50
50=5\times 5\times 2=5^2\times 2^1
Total no. of factors are
=(2+1)\times (1+1)=6
How many two-digit prime numbers are there having the digit
3
in their units place?
Report Question
0%
10
0%
8
0%
6
0%
5
Explanation
2
digit prime nos. having
3
in their units place are-
13,23,43,53,73
\therefore
There are
5
such nos.
The factor of 252 is:
Report Question
0%
2
0%
5
0%
11
0%
10
Explanation
252 = 2 \times 2 \times 3 \times 3 \times 7
.
The prime factors of
252
are
2,3,7
.
Thus the answer will be A.
A number is divisible by
9
, if the sum of the digits of the number is divisible by _______ .
Report Question
0%
3
0%
9
0%
6
0%
2
Explanation
A number is divisible by 9 if the sum of the digits of the number is divisible by
9
.
For example
81
is divisible by
9
as
8 + 1 = 9
is divisible by
9
.
So, option B is correct.
A student was asked to find the sum of all the prime numbers between
10
and
40.
He found the sum as
180.
Which of the following statements is true?
Report Question
0%
He missed one prime number between
10
and
20
0%
He missed one prime number between
20
and
30
0%
He added one extra prime number between
10
and
20
0%
None of these
Explanation
Prime numbers between
10
and
40
are
11,13,17,19,23,29,31,37
Sum of these prime numbers
= 180
\therefore
Option
D
is correct.
Which of the following is divisible by
9
?
Report Question
0%
75636
0%
89321
0%
75637
0%
75632
Explanation
Number are divisible by
9
if sum of the all the digits present in it , is divisible by
9
.
(a)75636
\Rightarrow 7+5+6+3+6=27
and
27
is divisible by 9.
Hence,
75636
is divisible by
9
(b)89321
\Rightarrow 8+9+3+2+1=23
and
23
is not divisible by
9
.
So,
89321
is not divisible by
9
.
(c)75637
\Rightarrow 7+5+6+3+7=28
and
28
is not divisible by
9
.
So,
75637
is not divisible by
9
.
(c)75632
\Rightarrow 7+5+6+3+2=26
and
26
is not divisible by
9
.
So,
75632
is not divisible by
9
Which of the following number is divisible by
6
?
Report Question
0%
3792
0%
5634
0%
9832
0%
3684
Explanation
The sum of the digits of the number should be divisible by
3
and the number should be even.
For option A:
3 + 7+ 9+ 2 =21
which is divisible by
3
and number is even. so answer A is right.
The sum of prime numbers, out of the numbers
17, 8, 21, 13, 41, 2, 27, 31, 51
is:
Report Question
0%
125
0%
102
0%
104
0%
155
Explanation
Prime numbers out of
17,8,21,13,41,2,27,31,51
are
17,13,41,2,31
.
Sum of prime numbers
= 17+13+41+2+31=104
.
Which of the following numbers is divisible by
9
?
Report Question
0%
8576901
0%
96345210
0%
67594310
0%
none of these
Explanation
We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Since sum of its digits
= 8 + 5 + 7 + 6 + 9 + 0 + 1 = 36
36
is divisible by
9
Option (a) is the correct answer
Which of the following numbers is divisible by
9
?
Report Question
0%
972063
0%
730542
0%
785423
0%
561284
Explanation
We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Sum of digits
= 9 + 7 + 2 + 0 + 3 = 27
which is divisible by
9
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