Question

find the hcf using euclid division lemma [1] 90 and 28​

Answer 1

Given :-

• We are given the Number s 90 & 28

To Find :-

• Their HCF?

Solution :-

Euclid's Division Lemma

Euclid's Division Lemma states a simple concept that then Product of the divisor and the quotient+the remainder will give us the dividend

$\displaystyle\sf :\implies \dfrac{A}{B} = Q+R$

$\displaystyle\sf :\implies A = B\times Q+R$

$\displaystyle\sf :\implies A = B(Q)+R$

Where,

✭ A = Dividend

✭ B = Divisor

✭ Q = Quotient

✭ R = Remainder

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

So now on calculating,

• 90 > 28

$\displaystyle\sf \dashrightarrow A = B(Q)+R$

$\displaystyle\sf \dashrightarrow 90 = 28(3)+6$

$\displaystyle\sf \dashrightarrow 28 = 6(4)+4$

$\displaystyle\sf \dashrightarrow 6 = 4(1)+2$

$\displaystyle\sf \dashrightarrow\underline{\boxed{\sf 4 = 2(2)+0 }}$

$\displaystyle\therefore\:\underline{\sf HCF(90,28) \ is \ 2}$

Answer 2

Answer :-

★ HCF of 90 and 28 = 2

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★Concept :-

Here, the concept of Euclid Division Lemma is used. According to this, two numbers a and b are related to each other in a unique order such that

a = bq + r

where, a is the Dividend, b is the Divisor, q is the Quotient and r is the Remainder.

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★ Solution :-

Given,

• Two numbers are : 90 and 28

Since 90 is greater than 28, then we have to divide 90 by 28. This division takes place using Long Division Method.

Now we are going to form our equation using these values and Euclid's Division Lemma. There,

• a is the dividend that is 90

• b is the divisor that is 28

• q is the quotient that comes out everytime on division of 90 ÷ 28

• r is the remainder that comes out everytime on 90 ÷ 28.

So, using all these informations, we get,

a = bq + r

On dividing 90 first time by 28, we get,

✒ 90 = 28(3) + 6

• Now the divisor is dividend and remainder is quotient. This way the next steps also follow until we get remainder = 0

✒ 28 = 6(4) + 2

✒ 6 = 2(3) + 0

Here we got our remainder that is equal to 0.

Hence, the last remaining Divisor is 2. Then definitely it will only be the HCF.

✳ So our HCF of 90 and 28 = 2

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★ More to know :-

• Euclid's Division Lemma states that when two numbers are given in the form of Division, then last quotient obtained from long division method is the HCF of the two numbers.

• HCF stands for Highest Common Factor which is the greatest factor of two or more numbers.

• LCM stands for Lowest Common Multiple which the least number multiplied to two or more numbers to make them equal.

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