Question

If HCF of 408 and 1032 is expressible in the form of 1032m - 408 x 5, then find m

Answer 1

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Answer 2

$\huge \fbox \red{Solution:}$

Firstly, the HCF of 408 and 1032 is to be found.

By applying Euclid’s division lemma, we get

1032 = 408x 2 + 216.

Here, the remainder ≠ 0. So apply Euclid’s division lemma on divisor 408 and remainder 216

408 = 216 x 1 + 192.

As the remainder ≠ 0, again apply division lemma on divisor 216 and remainder 192

216 = 192 x 1 + 24.

Again the remainder ≠ 0. So, apply division lemma again on divisor 192 and remainder 24

192 = 24 x 8 + 0.

Now, it is seen that the remainder is 0.

Hence, the last divisor is the H.C.F of 408 and 1032 i.e., 24

So, this HCF is expressed as a linear combination that is,

24 = 1032m - 408 x 5

1032m = 24 + 408 x 5

1032m = 24 + 2040

1032m = 2064

m = 2064/1032

∴ m = 2

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