1. Determine the length of the longest tape that can be used to measure
exactly a hall of dimensions 14 m 25 cm, 5 m 50 cm, and 6 m.
[ Hint: Convert m and cm into cm.)
Answers
Given, Dimensions of hall i.e 14m 25cm and 5m50cm
- To find, Longest tape
Solution :
- Convert m into cm
★ 1m = 100 cm
→ 14m25cm = 1400 + 25 = 1425 cm
→ 5m50cm = 500 + 50 = 550 cm
→ 6m = 600cm
We need to find H. C. F of 1425, 550 and 600 by prime factorisation
3|1425
5|475
5|95
19|19
|1
- 1425 = 3 × 5 × 5 × 19
5|550
5|110
2|22
11|11
|1
- 550 = 5 × 5 × 2 × 11
2|600
2|300
2|150
3|75
5|25
5|5
|1
- 600 = 2 × 2 × 2 × 3 × 5 × 5
5 × 5 is common in 1475,550 and 600
•°• HCF of (1475,550, 600) is 25
•°• The measure of the longest tape is 25 cm
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Given :-
Dimensions 14 m 25 cm, 5 m 50 cm, and 6 m.
To Find :-
Length of longest tape
Solution :-
We know that
1 m = 100 cm
14 m 25 cm = 14 × 100 + 25 = 1400 + 25 = 1425 cm
5 m 50 cm = 5 × 100 + 50 = 500 + 50 = 550 cm
6 m = 6 × 100 = 600 cm
Now
Finding HCF
Prime factorization of 1425 = 3 × 5 × 5 × 19 = 3 × 5² × 19
Prime factorization of 550 = 2 × 5 × 5 × 11 = 2 × 5² × 11
Prime factorization of 600 = 2 × 2 × 2 × 3 × 5 × 5 = 2³ × 3 × 5²
Therefore
Highest Common factor of 1425,550 and 600 is 5² or 25