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Step2247 [10]
3 years ago
13

ing%20%5C%3A%20e.d.l%20%5C%3A%20%5C%5C%20%28%20%5C%3A%20Euclid%27s%20%5C%3A%20division%20%5C%3A%20lemma%20%5C%3A%20%29" id="TexFormula1" title="Find \: H.C.F \: of \: \\ 900 \: , 270 \\ using \: e.d.l \: \\ ( \: Euclid's \: division \: lemma \: )" alt="Find \: H.C.F \: of \: \\ 900 \: , 270 \\ using \: e.d.l \: \\ ( \: Euclid's \: division \: lemma \: )" align="absmiddle" class="latex-formula">
H.C.F of 900 & 270 ​
Mathematics
2 answers:
wlad13 [49]3 years ago
6 0
<h2>See Above Attachment ⇡</h2>

\Large  \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}}  \: \red \mid

<h3>We know that , </h3>

As per Euclid Division Algorithm.

\longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \:  =  \: bq \:  +  \:  r \: }}}}}

  • a denotes dividend

  • b denotes divisor

  • q denotes quotient

  • r denotes remainder

<h2>◆━━━━━▣✦▣━━━━━◆</h2>

<h3>Using Euclid Division Algorithm</h3>

\large\bf{\purple{ \hookrightarrow \: }} \tt \: \: 900 \:  =  \: 270 \:  \times  \: 3 \:  +  \: 90

<h3>Here ,</h3>

\large\bf{\orange{ \implies \: }} \: \:r  \:  \neq \: 0

Again Applying Euclid Division Algorithm

\large\bf{\purple{ \hookrightarrow \: }} \tt \:  270 \:  =  \: 90 \:  \times  \: 3 \:  +  \: 0

<h3>Here ,</h3>

\large\bf{\orange{ \implies \: }} \: \:r  \:   =   \: 0

As the reminder is 0 , 90 will be the greatest common divisor for the two given numbers.

<h2>So,</h2>

{\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \:  =  \: 90}}}}}}

<h2>◆━━━━━▣✦▣━━━━━◆</h2>

brilliants [131]3 years ago
5 0

Answer:

  • 90

Step-by-step explanation:

<u>Factorize both numbers:</u>

  • 900 = 2*2*3*3*5*5
  • 270 = 2*3*3*3*5

<u>Common factors are:</u>

  • 2*3*3*5

<u>So HCF is:</u>

  • HCF(900, 270) = 2*3*3*5 = 90
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