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noname [10]
3 years ago
12

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

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
8 0

\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

<u>Work</u><u> </u><u>out</u><u>:</u>

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}}}}

<u>━━━━━━━━━━━━━━━━━━━━</u>

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Answer:

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