Find the length of the longest tape that can be used to measure the exactly the length 4 m 20 cm, 2 m 40 cm and 3 m 60 cm.

Given: 4 m 20 cm, 2 m 40 cm and 3 m 60 cm.

To find: Here we have to find the length of the longest tape that can be used to measure the exactly the length 4 m 20 cm, 2 m 40 cm and 3 m 60 cm.

Solution:

First convert the lengths into cm. We know that,

1 m = 100 cm

Now,

4 m 20 cm = 420 cm

2 m 40 cm = 240 cm

3 m 60 cm = 360 cm

To find the length of the longest tape we just have to find the HCF of 420, 240 and 360.

Writing down all the numbers as a product of their prime factors:

The prime factors of 420 are: 2 $\times $ 2 $\times $ 3 $\times $ 5 $\times $ 7

The prime factors of 240 are: 2 $\times $ 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $ 5

The prime factors of 360 are: 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $ 3 $\times $ 5

Product of all common prime factors: 2 $\times $ 2 $\times $ 3 $\times $ 5 = 60

HCF (420, 240, 360) = 60

The length of the longest tape is 60 cm which can be used to measure exactly the length 4 m 20 cm, 2 m 40 cm and 3 m 60 cm.

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Updated on: 10-Oct-2022

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