# Free Factors and Multiples 02 Practice Test - 5th Grade

___ is a pair of co-prime numbers.

A. 12, 15
B. 7, 15
C. 22, 48
D. 24, 36

#### SOLUTION

Solution : B

If any two numbers Highest Common Factor is 1, then they are called co-prime to each other.

HCF of 12 and 15 is 3
HCF of 7 and 15 is 1
HCF of 22 and 48 is 2
HCF of 24 and 36 is 12

Therefore 7, 15 is a pair of co-prime numbers since they have an HCF of 1.

A factorization in which every factor is a prime number is called ___

#### SOLUTION

Solution :

Prime factorization is finding the factors of a number that are all prime. The prime factors of 15 are 3 and 5.

Which of the following is a factor pair of 24?

A. 2 and 13
B.  1 and 13
C. 3 and 12
D. 4 and 6

#### SOLUTION

Solution : D

4 and 6 form a factor pair of 24 as 4×6=24.

2 and 13 form a factor pair of 26 as 2×13=26.

1 and 13 form a factor pair of 13 as 1×13=13.

3 and 12 form a factor pair of 36 as 3×12=36.

The number 7 has ___ multiples.

A. 1
B. 10
C. Finite
D. Infinite

#### SOLUTION

Solution : D

To get multiples of any number, we multiply counting numbers with that number.
Since there are infinite counting numbers, multiples of any number are also infinite.

All the multiples of 9 are also the multiples of ___

A. 5
B. 3
C. 7
D. 6

#### SOLUTION

Solution : B

9=3×3
9 is a multiple of 3
Hence any multiple of 9 will also be a multiple of 3.

The difference between the largest factor and the smallest factor of 100 is ___

A. 99
B. 48
C. 49
D. 100

#### SOLUTION

Solution : A

The smallest factor of any number is 1 and the highest factor of any number is the number itself.
Therefore, the difference between the highest and the smallest factor of 100 is, 1001=99

72 books were arranged equally on 8 shelves. How many books are there on each shelf?

A. 18
B. 9
C. 8
D. 72

#### SOLUTION

Solution : B

Number of books = 72
Number of shelves = 8
Therefore, books on each shelf = 72 divided by 8  = 9

The product of two numbers is 228. If their HCF is 12, then what will be their LCM?

A. 20
B. 1
C. 19
D. 0

#### SOLUTION

Solution : C

HCF of two numbers × LCM of two numbers = Product of the two numbers
12×LCM=228
LCM =22812=19

What is the least number that is exactly divisible by 15, 10 and 16?

A. 16
B. 240
C. 60
D. 160

#### SOLUTION

Solution : B

The least number that is exactly divisible by 15, 10 and 16 is the LCM of the three numbers.

215,10,16215,5,8215,5,4215,5,2315,5,155,5,11,1,1
LCM of 15, 10 and 16 =2×2×2×2×3×5=240

What is the sum of the first 5 prime numbers?

A. 17
B. 25
C. 28
D. 39

#### SOLUTION

Solution : C

First five prime numbers are: 2, 3, 5, 7, 11
Product of first five prime numbers is 2+3+5+7+11=28