Question

anup estimates that the global market for smart urban services will be $400 billion per annum by 2020.using this information calculate h.c.f of 400and 2020 by euclids division method

Answer 1

Hi ,

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Euclid's Division Lemma:
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Let a and b be any two postive

integers.

Then there exist two unique whole

numbers q and r such that

a = bq + r ,

0 less or equal to ' r ' < b

Alternatively ,

Dividend = divisor × quotient +

remainder

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According to the problem ,

400 , 2020 , start with the larger

integer, that is 2020.

Apply the division lemma to 2020

and 400 we get

2020 = 400 × 5 + 20

Since the remainder is not equal to

Zero.. We have to apply the division

lemma to 400 and 20

400 = 20 × 20 + 0

The remainder has now become zero

So our procedure stops.

Since the divisor at this stage is 20,

HCF of 2020 and 400 is 20.

I hope this will useful to you.

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Answer 2

Euclid division lemma :

a = bq + r

0 ≤ r < b

We need to find the HCF of 400 and 2020.

Applying euclid division lemma:-

2020 = 400 × 5 + 20

As reminder is 20,we need to proceed further.

400 = 20 × 20 + 0

As remainder is 0,we can not proceed any further.

And hence,HCF of 400 and 2020 is 20.

Hope it helps