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

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

A. 24
B. 12
C. 6
D. 1

#### 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

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.

The LCM of 3 and 5 is:

A. 30
B. 15
C. 35
D. 40

#### 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

The HCF of 13 & 7 is

A. 13
B. 7
C. 1
D. 91

#### 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.

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

A. 2
B. 1
C. 3
D. 5

#### 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.

How many common factors do 6 and 4 have?

A. 2
B. 3
C. 4
D. 6

#### 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.

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.

A. 32 cm
B. 24 cm
C. 40 cm
D. 48 cm

#### 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.

The largest factor of a number is ___

A. Number itself
B. 1
C. 3
D. 7

#### 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.

Except ___every number has at least two factors.

#### 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.

Find the LCM of 25, 50 and 100.

A. 25
B. 50
C. 75
D. 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