Question

find the hcf of 60 and 40 by Euclid's division lemma​

Answer 1

Answer:

60= 40×1 +20

40= 20×2 +0

HCF = 20

Answer 2

HCF(60, 40) = 20

Given:

Numbers 60 and 40

To find:

Find the hcf of 60 and 40 by Euclid's division lemma​

Solution:

Euclid's division lemma says that for any two positive integers, a and b where a>b then  'a = bq +r'

Here, q is Quotient and r is Reminder

Mathematically, we can write it as

      Dividend = (Divisor × Quotient) + Remainder  

Given numbers are 60 and 40, since 60 > 40

Divide 60 by 40,

Apply Euclid's division lemma​ law to given numbers

⇒ 60 = (40 × 1) + 20  

[ when 60 is divided by 20, Quotient = 1 and Reminder = 20 ]

Here, Reminder 20 $\neq$ 0

Apply Euclid's division lemma​ law to 40 and 20

⇒ 40 = (20 × 2) + 0  

Here, Reminder is equals to '0'  

Therefore, HCF(60, 40) = 20

#SPJ2