Question

If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 xp, then find the value of p.
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Answer 1

The value of p is -5.05.

Given: The HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 x p.

To find: We have to find the value of p.

Solution:

To determine the value of p we have to determine the HCF between 408 and 1032.

Then we have to equalise the HCF with the expression.

The HCF of 408 and 1032 is-

$408 = 4 \times 6 \times 17 \\ 1032 = 4 \times 6 \times 43 \\ 4 \times 6 = 24$

Equalising 24 with the expression we get-

$24 = 1032 \times 2 + 408p \\ 1 = 43 \times 2 + 17p \\ 17p = - 86 \\ p = - 5.05$

Thus the value of p is -5.05.

Answer 2

Answer:

-5

Step-by-step explanation:

By Euclid's division algorithm

dividend = divisor × quotient + remainder

a = bq+r

HCF of 408 and 1032

here a=1032

        b=408

        q=2

        r=216

1032=408×2+216

here a=408

        b=216

        q=1

        r=192

408=216×1+192

here a=216

        b=192

        q=1

        r=24

216=192×1+24

here a=192

        b=24

        q=8

        r=0

192=24×8+0

Since the remainder becomes 0 here,

so HCF of 408 and 1032 is 24

now 1032 x 2 + 408 × p =24

43×2+17p=1

86+17p=1

17p=1-86

17p=-85

p=-5

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