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Using Euclid's division algorithm, find the HCF of 455 and 42.
Given :
The given numbers are 455 and 42.
To find :
We have to the HCF of the given numbers 455 and 42 by using Euclid's division algorithm.
Solution :
By Euclid's division lemma,
$$Dividend = Divisor \times Quotient + Remainder$$
Here, $455 > 42$
So, divide 455 by 42,
$455 = 42 \times 10 + 35$
Remainder $= 35$
Repeat the above process until we will get 0 as the remainder.
Now, consider 42 as the dividend and 35 as the divisor,
$42 = 35 \times 1 + 7$
Remainder $= 7$
Now, consider 35 as the dividend and 7 as the divisor,
$35 = 7 \times 5 + 0$
Remainder $=0$
Therefore, HCF of 455 and 42 is 7.
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