Question

Using Euclid's division algorithm find the HCF of 408 and 1032

Answer 1

H. C. F = 24

Given :-

408 , 1032

To find :-

H. C. F using euclid division algorithm.

Answer:-

Euclid division algorithm / lemma :- Let a and b be a positive integer such that a > b . When a is divided by b their exists an unique integer q as quoteint and R as remainder satisfying the equation.

$a = bq + r (0 \leqslant R<0)$

Let b = 408 and a = 1032

by using euclid divine algorithm:-

$\implies$ $1032 = 408 \times2 +216$

$\implies$ $408 = 216 \times1 + 192$

$\implies$ $216 = 192 \times1 + 24$

$\implies$ $192 = 24 \times6 + 0$

As R = 0

then, Required H. C. F is = 24.

Answer 2

Answer:

Here is your answer

Step-by-step explanation:

Given numbers 1032 and 408

clearly 1032> 408

By euclid's division algorithm

1032 = 408 * 2 + 216

again, 216 is not equal to zero

408 =216 * 1 + 192

again, 192 is not equal to zero

216 =192 * 1 + 24

Here, 24 is not equal to zero

192 = 24 * 8 + 0

here the are a reminder is zero so it will be HCF of given number

HCF (1032, 408) = 8

Hope it is helpful to you