Question

Find the greatest possible length which can be used to measure exactly the lengths 4m 95cm, 9m, 16m 65cm?

Answer 1

Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.

495 = 32 x 5 x 11, 900 = 22 x 32 x 52, 1665 = 32 x 5 x 37.

H.C.F. = 32 x 5 = 45.

Hence, required length = 45 cm.


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Answer 2

Answer:

45 cm.

Step-by-step explanation:

Given:- Lengths are 4m 95cm, 9m, 16m 65cm.

To Find:- Greatest length which we can use to measure the exact given

                lengths.

Solution:-

First we will convert the lengths into it's smallest unit.

Acc. to our knowledge, 1 m = 100 cm.

∴ 4m 95cm = (400 + 95) cm = 495 cm,

  9m = 900 cm, and

  16m 65cm = (1600 + 65)cm = 1665 cm.

Here we need to find a common factor which can divide all the numbers.

An HCF i.e. Highest Common Factor of two or more numbers is the highest factor that can divide the numbers with leaving a remainder 0. It is also known as GCM (Greatest Common Measure) or GCD (Greatest Common Divisor) .

We can find HCF by using two methods i.e. Prime Factorization or by division method. In this case we will use prime factorization.

Factors of 495 = 11 × 3 × 3 × 5

Factors of 900 = 3 × 3 × 5 × 5 × 2 × 2

Factors of 1665 = 3 × 3 × 5 × 37

Therefore, HCF of 495, 900 and 1665 is 3 × 3 × 5 = 45.

Hence the greatest possible length which can be used to measure exactly the lengths 4m 95cm, 9m, 16m 65cm is 45 cm.

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