Question

*According to Euclid Division Algorithm, choose the correct statement for 95 and 9.*

1️⃣ 95 = 9 x 11 + 5
2️⃣ 9 = 95 x 1 + 5
3️⃣ 95 = 9 x 10 + 5
4️⃣ 9 = 9 x 10 + 5​

Answer 1

Given :- According to Euclid Division Algorithm, choose the correct statement for 95 and 9.*

1) 95 = 9 x 11 + 5

2) 9 = 95 x 1 + 5

3) 95 = 9 x 10 + 5

4) 9 = 9 x 10 + 5

Solution :-

Euclid’s division Lemma :-

• It tells us about the divisibility of integers.
• It states that any positive integer a can be divided by any other positive integer b in such a way that it leaves a remainder r .

Euclid's division Lemma states that for any two positive integers a and b there exist two unique whole numbers q and r such that :-

• a = bq + r, where 0 ≤ r < b.

Here,

• a = Dividend.
• b = Divisor.
• q = Quotient.
• r = Remainder.

Hence,

• The values r can take = 0 ≤ r < b.

we have given that,

• a = Dividend = 95
• b = Divisor = 9

So, 95 ÷ 9 :-

• 10 = b = quotient .
• 5 = r = remainder .

Therefore,

• a = bq + r
• 95 = 10 * 9 + 5
• 95 = 9 * 10 + 5 (Option 3) (Ans.)

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Answer 2

According to Euclid Division Algorithm, 95 = 9x10+5 is the correct statement.

Euclid Division Algorithm:

Two positive integers 'a' and 'b' there exits two unique integers 'q' and 'r' satisfies a=bq+r where 0 $\leq$ r $\leq$ b.

Divide 95 by 10.

10) 95 ( 9

    90

_____

    5

_____

Here,

Dividend is 95

Divisor is 10

Quotient is 9

Remainder is 5

Euclid Division Algorithm: = Dividend = Divisor x Quotient + Remainder

=> 95 = 9 x 10 + 5

Hence, the required answer is option 3.