Question

How to express the hcf of two numbers in the form of a linear equation ?
explain briefly and clearly with an example ?

Answer 1

Hello there!

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The equation we will use be:

a = bq + r

Where a is the divident, b is the divisor, Q the quotient and R be the remainder.

Let us say we have two numbers: 4 and 10.

we can write the divident: 10 (since 10 > 4)
as:

○ 10 = 4 x 2 + 2

this is nothing but the division of 10 by 4. The values received as replaced where b q and R were written.

Now take the b ( 4 ) in place of a ( 10 ) and take r ( 2 ) in place of b. ..... [1]

○ 4 = 2 x 2 + 0 ....... [2]

We keep doing [1] until we receive r = 0.

Now since r = 0 in [2], so 2 Is the HCF of 4 and 10.

□ Let us take another example. 12 and 20.

》 20 = 12 x 1 + 8

》 12 = 8 x 1 + 4

》 8 = 4 x 2 + 0

Since B = 4 and R = 0.
Therefore the HCF of 12 and 20 is 4.

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I hope it is very clear now!

Answer 2

Step-by-step explanation:

LET NUMBERS BE 52 AND 117

BY EUCLID'S DIVISION LEMMMA ,

117 = 52 * 2 + 13

52 = 13 * 4 + 0

THEREFORE ,  HCF = 13...

AS   117 = 52 * 2 + 13

        117 - (52*2) = 13

        (117*1) - (52*2) = 13

        52(-2) + 117(1) = 13

THEREFORE HCF OF 52 IS EXPRESSIBLE IN FORM OF LINEAR EQUATION

i.e. 52m + 117n

WHERE m = -2  AND n = 1