**A perfect number is:**

__Question:__**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. |

**Answer: Option A**

: 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 :

- 81, 82, 83, 84, 85, 86, 87
- 90, 91, 92, 93, 94, 95, 96
- 65, 67, 68, 69, 70, 71, 72
- 46, 47, 48, 49, 50, 51, 52

**Answer: Option B**

: B

All the numbers in the option:90, 91, 92, 93, 94, 95, 96have more than 2 factors, hence they are all composite numbers.

**___________ is a factor of every number and every number is a factor of _____________.**

__Question 3.__Choose the suitable pair from the following.

- 2, next number
- 2, itself
- 1, itself
- 1, next number

**Answer: Option C**

: 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 every number is a factor of itself.

- 1, 2, 3, 5, 7
- 2, 5, 9, 11, 17
- 19, 13, 11, 7, 3
- 23, 29, 39, 37, 43

**Answer: Option C**

: 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 is19, 13, 11, 7 and 3.

- 5, 7, 10, 11, 13, 17, 21 and 23
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
- 5, 7, 13, 14, 15, 16, 17 and 19
- 5, 7, 11, 13, 15, 16, 17, 20, and 25

**Answer: Option B**

: 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.

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