Question

the l,b,h of a room are 825cm, 675cm, 450cm respectively. determine the longest rod which can measure the three dimensions of the room exactly.

Answer 1

Hi,

Here is your answer,

Given,

Length = 825 cm 

Breadth = 675 cm

Height = 450 cm

Now, we need to do prime factorization,

→ P.F of  825 = 3 × 5 × 5 × 11

→ P.F of 675 = 3 × 3 × 3 × 5 × 5

→ P.F of 450 = 2 × 3 × 3 × 5 × 5

⊕ H.C.F(825,675,450) → 3 × 5 × 5

H.C.F. = 75

Therefore, the longest rod which can measure the three dimensions of the room exactly is 75.


Hope it helps you !