Question

find the HCF of 4032 & 262 by using euclid's division algorithm​

Answer 1

Answer:

HCF of 4032 & 262 = 2

Step-by-step explanation:

To find,

HCF of 4032 & 262

Recall the concepts

To find the HCF of two numbers 'a' and 'b'(a>b) using Euclid's division algorithm​,

divide 'a' by 'b', we get 'q' as quotient and 'r' as a reminder such that

a = pb + r, 0≤r<b.

if r  = 0, then the HCF (a,b) = b

If r ≠ 0, then continue the process by applying the division lemma for b and r, till we get the reminder 0

Then the HCF will be the last non-zero reminder

Solution:

Here, a = 4032 and b = 262

Divide 4032 by 262

4032 = 262 × 15 +102

applying the division lemma continuously till we get a non-zero remainder

262 = 102 × 2 +58

102 = 58×1 + 44

58 = 44×1 + 14

44 = 14 ×3 +2

14 = 2×7 +0

The last non-  zero reminder is 2

Hence HCF of 4032 & 262 = 2

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Answer 2

Concept:

Division of Euclid Given two positive numbers, a and b, the lemma, or Euclid division procedure, claims that there are two distinct integers, q and r, which satisfy the equation a = bq + r, 0 r b.

Follow the instructions below to find the HCF of two positive integers, let's say c and d, with c > d:

Apply C and D to Euclid's division lemma in step 1. In order to determine c = dq + r, 0 r d, we find whole numbers q and r.

Step 2: D is the HCF of c and d if r = 0. If r ≠ 0, apply the division lemma to d and r.

Step 3: Repeat the previous steps up until the remainder is zero. The necessary HCF will serve as the divisor at this point.

Given information:

$4032 , 262$ are the numbers given for HCF.

To find:

We need to find the HCF of $4032 , 262$ .

Solution:

Let,

a = $4032$

b = $262$

Divide a by b.

$4032=262*15+102$

Apply euclid's division lemma.

$262=102*2+58\\102=58*1+44\\ 58=44*1+14\\44=14*3+2\\14=2*7+0$

The last non- zero remainder is $2$.

Hence, the HCF of $4032,262$ is $2$ .

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