Question

The greatest possible length which can be used to measure exactly the lengths 1m 92cm,3m 84cm ,23m 4cm

Answer 1

We need to find the HCF of 1m92cm, 3m 84cm, 23m4cm.
1m92cm =192cm   =2X2X2X2X2X2         X3
3m84cm=384cm   =2X2X2X2X2X2X2    X3
23m4cm=2304cm=2X2X2X2X2X2X2X2X3X3
HCF=2X2X2X2X2X2X3
       =192cm
Therefore 1m92cm of a rod can be placed in the room of dimensions 1m92cm, 3m 84cm, 23m4cm.
HOPE THIS HELPS!!!!!

Answer 2

The greatest possible length which can be used to measure exactly the lengths 1m 92cm, 3m 84cm and 23m 4cm is 1m 92cm.

Given:

Three lengths 1m 92cm, 3m 84cm and 23m 4cm.

To find:

The greatest possible length can be used to measure exactly the given lengths.

Solution:

To answer this question, we will follow the following steps:

As given in the question, we have,

Three lengths 1m 92cm, 3m 84cm and 23m 4cm.

To find the greatest length, we will find the HCF of three lengths.

Now,

The factors of 1m 92cm or 192 cm

= 2 × 2 × 2 × 2 × 2 × 2 × 3

The factors of 3m 84 cm or 384 cm

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

The factors of 23m 4cm or 2304cm

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

So,

The highest common factor among three lengths = 2 × 2 × 2 × 2 × 2 × 2 × 3

= 192 cm

= 1 m 92 cm

Hence, the greatest possible length which can be used to measure exactly the lengths 1m 92cm, 3m 84cm and 23m 4cm is 1m 92cm.

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