Question

The length, breadth and height of a box are 25cm, 35cm

and 40cm respectively. Find the length of the longest tape

which can measure the three dimensions of the box exactly​

Answer 1

Answer:

Let us factorize all three given dimensions.

825 = 3 × 5 × 5 × 11

675 = 3 × 3 × 3 × 5 × 5

450 = 2 × 3 × 3 × 5 × 5

Hence, 3, 5 and 5 are the common prime factors here.

So, H.C.F =3 × 5 × 5

H.C.F = 75 cm

Therefore, we need 75 cm the longest tape to measure the three dimensions of the room.

Answer 2

Given :

• Length of the box = 25 cm
• Breadth of the box = 35 cm
• Height of the box = 40 cm

To find :

• Length of the longest tape which can measure the three dimensions of the box exactly.

Concept :

Here, we will find the highest common factor of the dimensions of the box. The highest common factor will be equal to the length of the longest tape which can measure the three dimensions of the box exactly.

★ How to find HCF?

→ HCF is also known as Highest common factor.

To find it :-

• Firstly, find the factors of the given numbers.
• The numbers which are found repeating in all the given numbers are multiplied and the resultant value is our highest common factor.

Let's do it →

Solution :

→ 25 = 5 × 5

→ 35 = 5 × 7

→ 40 = 2 × 2 × 2 × 5

Here, 5 is repeated in all the given numbers. So, 5 is the highest common factor.

HCF = 5

Therefore,

• The length of the longest tape which can measure the three dimensions of the box exactly is 5 cm.