# Free Playing with Numbers 01 Practice Test - 6th grade

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

Choose the suitable pair from the following.

A.

2, next number

B.

2, itself

C.

1, itself

D.

1, next number

#### SOLUTION

Solution : C

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

Therefore, 1 is a factor of every number and e
very number is a factor of itself.

Every number is a multiple of ______________ .

A.

5

B.

2

C.

itself

D.

100

#### SOLUTION

Solution : C

Every number is a multiple of itself .

A perfect number is:

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.

#### SOLUTION

Solution : 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 of its factors 1, 2, 3 and 6 is 12 i.e. twice of 6.

Perfect numbers are also defined as those numbers that equal the sum of all their factors including 1 but excluding the number itself.

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

The factors of 72 are __________________.

A.

5, 7, 10, 11, 13, 17, 21 and 23

B.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

C.

5, 7, 13, 14, 15, 16, 17 and 19

D.

5, 7, 11, 13, 15, 16, 17, 20, and 25

#### SOLUTION

Solution : B

72=1×72

=2×36

=3×24

=4×18

=6×12

=8×9

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Which of the following is the largest two-digit multiple of 19?

A.

85

B.

76

C.

96

D.

95

#### SOLUTION

Solution : D

19 × 1 = 19
19
× 2 = 38
19
× 3 = 57
19
× 4 = 76
19
× 5 = 95
19
× 6 = 114
Hence, the largest two-digit multiple of 19 is 95.

Choose the option which contains set of prime numbers.

A.

1, 2, 3, 5, 7

B.

2, 5, 9, 11, 17

C.

19, 13, 11, 7, 3

D.

23, 29, 39, 37, 43

#### SOLUTION

Solution : 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 correct option is
19, 13, 11, 7 and 3.

The largest 3 digit composite number is:-

A.

1000

B.

999

C.

989

D.

949

#### SOLUTION

Solution : 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)

Composite numbers have more than _______ factors.

A.

6

B.

10

C.

15

D.

2

#### SOLUTION

Solution : D

Composite numbers have more than 2 factors.

For example, factors of 4 are 1, 2 and 4.

7 consecutive composite numbers less than 100 are -

A.

81, 82, 83, 84, 85, 86, 87

B.

90, 91, 92, 93, 94, 95, 96

C.

65, 67, 68, 69, 70, 71, 72

D.

46, 47, 48, 49, 50, 51, 52

#### SOLUTION

Solution : B

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

Which of the following numbers are divisible by 11 and 9 respectively?

A.

10000001, 459756

B.

9000001, 45975

C.

4569874, 547952

D.

4568947, 97455

#### SOLUTION

Solution : A

To check the divisibility of a number by 11, we find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is 0 or a number divisible by 11, then the number is divisible by 11.
For 10000001,

Sum of digits at odd places = 1

Sum of digits at even places = 1

difference = 1 - 1 = 0

Hence, 10000001 is divisible by 11

For divisibility by 9 - if the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
The sum of digits of 459756 is 36 which is divisible by 9.
Hence, 459756 is divisible by 9.