Question

Q4) Using Euclid's algorithm, find the HCF of 240 and 228​

Answer 1

$\LARGE{ \underline{ \boxed{ \purple{ \rm{Solution : )}}}}}$

Euclid's division lemma : Let a and b are two positive integers. There exist unique integers q and r such that

a = bq + r, 0 $\leqslant$ r < b

Or We can write it as,

Dividend = Divisor × Quotient + Remainder

Work out:

Given integers are 240 and 228. Clearly 240 > 228. Applying Euclid's division lemma to 240 and 228,

⇛ 240 = 228 × 1 + 12

Since, the remainder 12 ≠ 0. So, we apply the division dilemma to the division 228 and remainder 12,

⇛ 228 = 12 × 19 + 0

The remainder at this stage is 0. So, the divider at this stage or the remainder at the previous age i.e 12

$\large{ \therefore{ \boxed{ \sf{HCF \: of \: 240 \: \& \: 228 = 12}}}}$

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