Question

find the HCF of numbers 72 and 96 by Euclid division algorithm and Express it in the form 96 M + 72 n where M and n are integers​

Answer 1

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❄Question:-Find the HCF of 72 & 96 by Euclid division algorithm and express it in form 96 m+72 n where m and n are some integers.
❄Answer: -
According to Euclid’s Division Lemma, if a and b are any two positive integers then there exist two unique whole numbers q and r such that
a=b q+r
where 0 ≤ r < b
Here, a is called the dividend,
b is called the divisor,
q is called the quotient and
r is called the remainder.
So, apply the lemma on 96 and 72.
We get,
96=(72×1) +24.......... (i)
Since the remainder is not zero.
Apply the lemma again on 72 and 24.
We get,
72 = (24 × 3) + 0
We have finally got remainder as 0.
⇒ HCF (96, 72) = 24
Now, we need to express the HCF in the form 96m + 72n, where m and n are integers.
So, take equation (i),
96 = (72 × 1) + 24
⇒ 24 = 96 – (72 × 1)
⇒ 24 = 96 (1) – 72 (1)
⇒ 24 = 96 (1) + 72 (-1)
Thus, 24 is expressed as
24 = 96 (1) + 72 (-1)
Where, m = 1 & n = -1 are integers.
HOPE IT HELPS YOU
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