Question

Length, breadth and height of a room are 735 cm, 625 cm, 415 cm. Find the length of the largest scale measuring instruments which can measure all the three dimensions.

Answer 1

Hint: Here, find the HCF of length, breadth and height of room i.e., HCF of (735, 625, 415).
HCF will be the largest scale measure instrument which can measure three dimensions.

Complete step-by-step answer:
 Given, length of room = 735 cm
Breadth of room = 625 cm
Height of room = 415 cm
The length of the largest scale measuring instruments which can measure all the three dimensions
= HCF of (735, 625, 415)
Now, 735 = 5 × 3 × 7 × 7
625 = 5 × 5 × 5 × 5
415 = 5 × 83
$ \Rightarrow $ HCF of (735, 625, 415) = 5
Therefore, the length of the largest scale measuring instruments which can measure all the three dimensions 735 cm, 625 cm, 415 cm is 5 cm.

Note: In these types of questions, use concept of HCF (Highest common factor). HCF of two numbers means both the numbers are multiple of the resulting HCF or HCF can exactly divide both the numbers.
Alternatively, we can find HCF of 735 and 625 and then HCF of 415 and resultant HCF of (735 and 625) . This also gives us the same result.
HCF of (735 and 625)
735 = 5 × 3 × 7 × 7
625 = 5 × 5 × 5 × 5
HCF of (735 and 625) = 5
Now, HCF of (5 and 415)
5 = 5 × 1; 415 = 5 × 83
$ \Rightarrow $ HCF of (5 and 415) = 5
Therefore, HCF of (735, 625, 415) = 5.