Question

(iii) The length, breadth, height of a room are 6m 80 cm, 5m 10 cm and 3 m 40 cm respectively. Find the longest tape which can measure the dimensions of the room exactly.

Answer 1

Hcf of the dimension = the longest tape which can measure the dimension of the room exactly
first we should convert the dimension into cm or m
and Thn we should find the Hcf of each dimension
680=2*2*2*5*17
510=2*5*3*17
340=2*2*5*17
Hcf =170
the length of longest tape is 170cm
or
1m70cm

Answer 2

Given,

Length = 6m 80 cm = 680cm

Breadth = 5m 10cm = 510cm

Height = 3m 40cm = 340cm

To find,

the longest tape which can measure the dimensions of the room exactly.

Solution,

Length = 6m 80 cm

Breadth = 5m 10cm

Height = 3m 40cm

To convert metres into centimeters we multiply it with 100

So

Length = 6m 80 cm

= 6 x 100 + 80

= 680cm

Breadth = 5m 10cm

= 5 x 100 + 10

= 510cm

Height = 3m 40cm

= 3 x 100 + 40

= 340cm

Now we find the prime factors of the numbers. So it will be,

Length = 680 = 2 x 2 x 2 x 5 x 17

Breadth = 510 = 2 x 5 x 3 x 17

Height = 340 = 2 x 2 x 5 x 17

The HCF, the Highest Common Factor of these numbers will be,

HCF = 2 x 5 x 17

= 170cm or 1m 70cm

Thus, the longest tape which can measure the dimensions of the room exactly is 1m 70cm long