Find the length of the longest tape that can be used to measure exactly the lengths of 4 m 20cm, 240 cm and 360 cm.

Given :

The given lengths are 4 m 20cm, 240 cm and 360 cm.

To find :

We have to find the length of the longest tape that can be used to measure exactly the given lengths.

Solution :

We know that, $1 m = 100 cm$

$4 m 20 cm = 400 cm + 20 cm = 420 cm$. 

Highest common factor of 420, 240, 360 is the length of the longest tape that can measure the given lengths exactly.

Prime factors of $420 = 2 \times 2 \times 3 \times 5 \times 7 = 2^2 \times 3 \times 5 \times 7$

Prime factors of $240 =2 \times 2 \times 2 \times 2 \times 3\times 5 = 2^4 \times 3 \times 5$

Prime factors of $360 =2 \times 2 \times 2 \times 3 \times 3\times 5 = 2^3 \times 3^2 \times 5$

$$HCF = Product of common prime factors with smallest powers$$.

$HCF = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$

The length of the longest tape that can be used to measure exactly the lengths 4m 20cm, 240 cm and 360 cm is 60 cm. 

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Updated on: 10-Oct-2022

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