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[tex]Find \: H.C.F \: of \: \\ 900 \: , 270 \\ using \: e.d.l \: \\ ( \: Euclid's \: division \: lemma \: )[/tex]
H.C.F of 900 & 270 ​

Respuesta :

mhanifa

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

See Above Attachment ⇡

[tex]\Large \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}} \: \red \mid[/tex]

We know that ,

As per Euclid Division Algorithm.

[tex] \longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \: = \: bq \: + \: r \: }}}}} [/tex]

  • a denotes dividend

  • b denotes divisor

  • q denotes quotient

  • r denotes remainder

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Using Euclid Division Algorithm

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

Here ,

[tex]\large\bf{\orange{ \implies \: }} \: \:r \: \neq \: 0[/tex]

Again Applying Euclid Division Algorithm

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

Here ,

[tex]\large\bf{\orange{ \implies \: }} \: \:r \: = \: 0[/tex]

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

So,

[tex]{\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \: = \: 90}}}}}}[/tex]

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