Question

HCF of 396 and 72 by using division of lemma​

Answer 1

Answer: 36 is the HCF

HOPE THIS HELPS.........

Answer 2

Question:-

To find the HCF of 396 and 72 using division of lemma.

Solution:-

According to Euclid's Division Lemma,

$\sf{a = b\times q + r \:\:\:\:where 0\leq r < b}$

Here,

a = 396 and b = 72

Now, we need to divide 396 by 72,

${\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\put(2.6,5.5){\large\sf 72 \bigg)}\put(3.7,5.5){\large\sf 396}\put(4.5,5.5){\large\sf\bigg( 5}\put(3.7,4.8){\large\sf 360}\put(3.8,3.8){\large\sf 36}\put(3.2,6){\line(5,0){1.6}}\put(3.2,4.5){\line(5,0){1.6}}\end{picture}}$

Hence,

$\sf{396 = 72\times5 + 36}$

Here,

$\sf{r \neq 0}$

So we need to apply Euclid's Division Lemma again,

Now,

a = 72 and b = 36

${\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\put(2.6,5.5){\large\sf 36 \bigg)}\put(3.7,5.5){\large\sf 72}\put(4.5,5.5){\large\sf\bigg( 2}\put(3.7,4.8){\large\sf 72}\put(3.8,3.8){\large\sf 0}\put(3.2,6){\line(5,0){1.6}}\put(3.2,4.5){\line(5,0){1.6}}\end{picture}}$

Hence,

$\sf{72 = 36\times2 + 0}$

Here,

$\sf{r = 0}$

Hence, the HCF of 396 and 72 is 36.

Important Information:-

In Euclid's Division Lemma,

• $\sf{a\:stands\:for\:Dividend}$
• $\sf{b\:stands\:for\:Divisor}$
• $\sf{q\:stands\:for\:Quotient}$
• $\sf{r\:stands\:for\:Remainder}$
• We need to apply the Division Lemma till r = 0.