Question

If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5, find m.

Answer 1

SOLUTION :

First we need the H.C.F of 408 and 1032 .

Here 408 < 1032

Let a = 1032 and b= 408

1032 = 408x 2 + 216.

[By applying division lemma, a = bq + r]

Here, remainder = 216 ≠ 0, so take new dividend as 408 and new divisor as 216.

Let a = 408 and b= 216

408 = 216 x 1 + 192.

[By applying division lemma, a = bq + r]

Here, remainder = 192 ≠ 0, so take new dividend as 216 and new divisor as 192.

Let a = 216 and b= 192

216 = 192 x 1 + 24.

[By applying division lemma, a = bq + r]

Here, remainder = 24 ≠ 0, so take new dividend as 192 and new divisor as 24

Let a = 192 and b= 24

192 = 24 x 8 + 0.

Here, remainder is zero and divisor is 24

Hence ,H.C.F. of 408 and 1032 is 24

Therefore,

24 = 1032 m -  408 x 5

1032m = 24 + 408 x 5

1032m = 24 + 2040

1032m = 2064

m = 2064/1032

m = 2

Hence, the value of m is 2.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Given integers are 408 and 1032.

Here, 1032 > 408.

(i)

1032 = 408 * 2 + 216.

Here, remainder is ≠ 0. Apply division on 408(Quotient) and 216(Remainder).

(ii)

408 = 216 * 1 + 192

Here, remainder ≠ 0. Apply division on 216 and 192.

(iii)

216 = 192 * 1 + 24

Here, remainder ≠ 0. Apply division on 192 and 24.

(iv)

192 = 24 * 8 + 0.

Here, remainder = 0.

So, HCF of 408 and 1032 is 24.

Now,

⇒ HCF = 1032m - 408 * 5

⇒ 24 = 1032m - 2040

⇒ 24 + 2040 = 1032m

⇒ 2064 = 1032m

⇒ m = 2064/1032

⇒ m = 2.

Therefore, the value of m = 2.

Hope it helps!