# Free Factors and Multiples 02 Practice Test - 4th Grade

### Question 1

The least number which is exactly divisible by 6, 12, 24 is ___.

#### SOLUTION

Solution :A

The least number which is exactly divisible by 6, 12, 24 is the LCM of the 3 numbers.

26,12,2423,6,1223,3,633,3,31,1,1

LCM of 6, 12 and 24

=2×2×2×3=24

### Question 2

The number 7 has ___ multiples.

#### 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.

### Question 3

The LCM of 3 and 5 is:

#### SOLUTION

Solution :B

Factors of 3: 1, 3

Factors of 5: 1, 5

3 and 5 are co-prime numbers because 1 is their only common factor.

LCM of co-prime numbers is equal to the product of the numbers.

So,

LCM of 3 , 5=3×5=15

### Question 4

The HCF of 13 & 7 is

#### SOLUTION

Solution :C

Factors of 13: 1, 13

Factors of 7: 1, 7

The only common factor is 1.

Hence the HCF of 13 and 17 is 1.

### Question 5

Find the greatest number that divides 2, 3 & 6 exactly.

#### SOLUTION

Solution :B

The greatest number that can divide 2, 3 and 6 exactly is their HCF.

Factors of 2:1, and 2

Factors of 3:1, and 3

Factors of 6:1, 2, 3, and 6

So, the common factor is 1 which is also the HCF.

### Question 6

How many common factors do 6 and 4 have?

#### SOLUTION

Solution :A

Factors of 6: 1, 2, 3, 6

Factors of 4: 1, 2, 4

Common factors : 1 ,2

Hence, 6 and 4 have 2 common factors.

### Question 7

Three measuring rods are 6 cm, 4 cm and 8 cm long. Find the shortest length that can be measured exactly by each one of these rods.

#### SOLUTION

Solution :B

To find the shortest length that can be measured exactly by using each one of these rods, we need to find the LCM of their lengths.

26,4,823,2,423,1,233,1,11,1,1

LCM =2×2×2×3=24 cm

Therefore, 24 cm is the shortest length that can be measured exactly by each one of these rods.

### Question 8

The largest factor of a number is ___

#### SOLUTION

Solution :A

The largest factor of a number is the "number itself".

For example, the highest factor of 48 is 48.

The lowest factor of any number is 1.

### Question 9

Except

#### SOLUTION

Solution :1 is an unique number. It is neither a prime number nor a composite number.

1 is the only number that does not have two factors.

### Question 10

Find the LCM of 25, 50 and 100.

#### SOLUTION

Solution :D

Using the prime factorization method:

225,50,100525,25,5055,5,1021,1,21,1,1

LCM of 25, 50 and 100 =2×5×5×2=100