Question

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 ​

Answer 1

See Above Attachment ⇡

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

We know that ,

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

◆━━━━━▣✦▣━━━━━◆

Using Euclid Division Algorithm

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

Here ,

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

Again Applying Euclid Division Algorithm

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

Here ,

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

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

So,

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

◆━━━━━▣✦▣━━━━━◆

Answer 2

Answer:

• 90

Step-by-step explanation:

Factorize both numbers:

• 900 = 2*2*3*3*5*5
• 270 = 2*3*3*3*5

Common factors are:

• 2*3*3*5

So HCF is:

• HCF(900, 270) = 2*3*3*5 = 90