## Lakshya Education MCQs

Question: A perfect number is:
Options:
 A. a number whose sum of factors is equal to twice the number. B. a number whose sum of its digits is equal to the product of its digits. C. a number whose sum of  factors is equal to thrice the number. D. a number which is co-prime to every other number.
: A

A perfect number is a number for which the sum of all its factors is equal to twice the number. For example, 6 is a perfect number since the sum ofits factors 1, 2, 3 and 6 is 12 i.e. twice of 6.

Perfect numbers are also defined as those numbers that equalthe sum of all their factorsincluding 1 butexcluding the number itself.

Taking the same example of 6: sum of its factors excluding the numberitself i.e 6 = 1+2+3 = 6.

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## More Questions on This Topic :

Question 1. The largest 3 digit composite number is:-
1.    1000
2.    999
3.    989
4.    949
: B

Composite numbers are those numbers which are not prime numbers except 1. 1 is regarded as a unique number.
The largest 3 digit number is 999 and it is a composite number. (divisible by 3, 9 etc)
Question 2. 7 consecutive composite numbers less than 100 are -
1.    81, 82, 83, 84, 85, 86, 87
2.    90, 91, 92, 93, 94, 95, 96
3.    65, 67, 68, 69, 70, 71, 72
4.    46, 47, 48, 49, 50, 51, 52
: B

All the numbers in the option:90, 91, 92, 93, 94, 95, 96have more than 2 factors, hence they are all composite numbers.
Question 3. ___________ is a factor of every number and every number is a factor of _____________.

Choose the suitable pair from the following.
1.    2, next number
2.    2, itself
3.    1, itself
4.    1, next number
: C

1 is an exact divisor of all the numbers.Also, any number is divisible byitself.

Therefore,1 is a factor of every number and e
very number is a factor of itself.
Question 4. Choose the option which contains set of prime numbers.
1.    1, 2, 3, 5, 7
2.    2, 5, 9, 11, 17
3.    19, 13, 11, 7, 3
4.    23, 29, 39, 37, 43
: C

Prime numbers have only two factors, 1 and the number itself. 1 is neither prime nor composite.

2 is the only even prime number.

9 and 39 have more than 2 factors, hence they are not prime numbers.

Considering all these, the correctoption is
19, 13, 11, 7 and 3.
Question 5. The factors of 72 are __________________.
1.    5, 7, 10, 11, 13, 17, 21 and 23
2.    1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
3.    5, 7, 13, 14, 15, 16, 17 and 19
4.    5, 7, 11, 13, 15, 16, 17, 20, and 25
: B

72=1×72 =2×36 =3×24 =4×18 =6×12 =8×9 Factors of 72 are1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and72.
Question 6. Composite numbers have more than _______ factors.

1.    6
2.    10
3.    15
4.    2