Free Factors and Multiples 01 Practice Test - 4th Grade 

Question 1

Which of the following is a factor pair of 26?

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

SOLUTION

Solution : A

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.

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

Question 2

The largest number which can divide 28 and 42 completely is ___.

A. 2
B. 3
C. 14
D. 7

SOLUTION

Solution : C

The largest number which can divide 28 and 42 completely is the HCF of the two numbers.

HCF of 28 and 42
=2×7=14 

Question 3

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

Question 4

The smallest number that is divisible by 2,4,6 is____

A. 8
B. 12
C. 9
D. 36

SOLUTION

Solution : B

The smallest number divisible by any 2 or more numbers is their least common multiple (LCM).
The multiples  of 2 : 2 , 4 , 6 , 8 , 10 , 12 , 14 .....
The multiples of 4:  4 , 8 , 12 , 16 , 20 ......
The multiples of 6: 6 , 12 , 18 , 24 .........
As you can see, 12 is the smallest multiple that is commom for all 3 numbers.
So, the LCM of 2, 4, 6 = 12

Question 5

Find the greatest number that divides 3 & 6 exactly.

A. 1
B. 3
C. 6
D. 12

SOLUTION

Solution : B

A number that divides 3 and 6 exactly is a common factor of 3 and 6.

∴ The greatest number that divides 3 and 6 is equal to their Highest Common Factor (HCF).

We need to find the HCF of 3 and 6.

Factors of 3 = 1 , 3
Factors of 6 = 1 , 2 , 3 , 6

The common factors of 3 and 6 are 1 and 3.

∴ The highest common factor of 3 and 6 is 3.
∴The greatest number that divides 3 and 6 exactly is 3.

Question 6

In which of the following cases, is the first number a factor of the second number?

A. 4, 38
B. 6, 52
C. 8, 96
D. 5, 33

SOLUTION

Solution : C

When 38 is divided by 4, the remainder is 2. So, 4 is not a factor of 38.
When 52 is divided by 6, the remainder is 4. So, 6 is not a factor of 52.
When 33 is divided by 5, the remainder is 3. So, 5 is not a factor of 33.
When 96 is divided by 8 the remainder is 0. So, 8 is a factor of 96.

Question 7

The ___ of two or more numbers is the least number which is exactly divisible by those numbers.

SOLUTION

Solution :

The LCM of two or more numbers is the least number which is exactly divisible by those numbers.                                                       

Example:  LCM of 4 and 6 is 12. So, 12 is the least number which is exactly divisible by 4 and 6.

Question 8

___ is a factor of every number.

SOLUTION

Solution :

One is the common factor for all the numbers.

Each number is divisible by one and the "number itself".

For example, 3 is divisible by both 1 and 3.

Question 9

The largest 2-digit prime number is ___

SOLUTION

Solution :

Prime numbers are numbers which are divisible by 1 and the "number itself",

So, 3 is a prime number as it is divisible by only 1 and 3.

99 is not a prime number as it is divisible by 1, 9, 11, 99.

98 is also not a prime number as it is divisible by 1, 2, 7, 49, 98.

The largest 2-digit prime number is 97, as it is divisible only by 1 and 97.

Question 10

Manu goes to dance class once in every 6 days, to karate class once in every 12 days and to art classes once in every 18 days. He attends all the three classes on 1st of April. On which day, will he attend all the 3 classes again?

A. 8th May
B. 7th May
C. 1st May
D. 21st April

SOLUTION

Solution : B

He will go to all the 3 classes on the day which is LCM of 6, 12, 18.

LCM =2×3×2×3=36
If he attends all the three classes on 1st of April, then he will attend all the three classes after 36 days which is 7th May.

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