Euclid's Division Lemma Extra Questions

04 Nov, 2021

Extra Questions On Euclids Division Lemma Given positive integers a and b there exist unique integers q and r satisfying a bq r where 0 r b Here we call a as dividend b as divisor q as quotient and r as remainder Dividend Divisor x Quotient RemainderIf in. This is because either k is even or if not then k 1 is even.

Use Euclid S Division Algorithm To Find The Hcf Of 726 And 275

To do this we choose the largest integer first ie.

Euclid's division lemma extra questions. If r0then what is the relationship between ab and q in abqr of euclid division lemma. 25 7 2 11 D. 4k 2 4k11 4k 2 4k 4kk1 Note that the product kk1 will always be even.

After division Quotient 43 and Remainder 2. Use Euclids division lemma to show that the cube of any positive integer is of the form 9m 9m 1 or 9m 8. Now here a 980 b 78 q 12 and r 44.

23 5 4 3. Comparing with a bq r. For any two positive integers a and b there exist unique integers q and r such that a bq r where 0 r b.

Use Euclid division lemma to show that any positive odd integer is of form 6q 1 or 6q 3 or 6q 5 where q is some integers. The process of dividing one integer by another in such a way that it produces a question a remainder which is smaller than the divisor. Let a is a positive integer and b 4.

The books are of the same size. Let us consider a 217 b 5 and make the division of 217 by 5 as under. In Euclids Division Lemma when abqr where ab are positive integers then what values r can take.

These books are to be packed in separate bundles and each bundle must contain the same number of books. We can write the result in following form by applying the Euclids Division Lemma method 58 9 x 6 4. The sum of squares of two consecutive multiples of 7 is 637.

In this chapter we have to study Euclids Division Lemma Euclids D. 25 25 1 0 B. By Euclids Division Lemma n can be written as n 2k1 kZ.

980 and then according to Euclid Division Lemma a bq r where 0 r b. Solve Easy Medium and Difficult level questions from Euclids Division Lemma. 25 7 3 4 C.

Thus n 2 1 2k1 2 1. Important Questions on Euclids Division Lemma is available on Toppr. Or x is a factor common of both 369 and 697.

Divide 217 by 5 as below. From the given Divisor 5. Step 2 - Use Euclids Division Lemma to find HCF of 369 and 697.

Use Euclids division lemma. Find hcf of72and 108divisions lemma. The basis of the Euclid Division Algorithm is Euclids Division Lemma.

Given positive integers a and b b 0 there exists unique integer numbers q and r satisfying a bq r 0 r b. 1What is Euclid Division Lemma. Prove Euclids Division Lemma.

E uclids Division Lemma Represents The Pair Of Integers 25 7. The question and remainder are unique under some conditions. 25 7 4 3 22.

CBSE Class 10 Maths Chapter 1 Extra MCQs 21. 17 5 3 2 Q2. 0 4 9.

If the HCF of 408 and 1032 is expressible in the form 1032m-4085 find m. Therefore according Euclids division lemma a3qr where 0r4 Therefore if r0 then a3q Or a33q327q3 Or a393q3 Or a39m where m3q3. In Questions number 2 4 and 5 also apply step by step Euclids Division Algorithms to prove the questions.

Apply Euclids Lemma on 697 with 369 as divisor 697 369 1 328 The remainder is not zero. State Euclids Division Lemma. In Questions number 1 we have to find HCF applying Euclids Division Lemma.

Important Questions Ask Doubt. Which is t he Number in the form Of 4p 3 if P is a Whole Number. Dear StudentsReal Numbers is a very interesting chapter in Class 10 Mathematics.

Now consider the divisor 78 and the remainder 44 apply Euclid division lemma again. Where a is called dividend b is called divisor q is called quotient r is called remainder. EUCLIDS DIVISION LEMMA OR EUCLIDS DIVISION ALGORITHM.

Because x is the largest such number x is the HCF of 369 and 697. Even or Odd D. A book seller has 28 Kannada and 72 English books.

Recall that the HCF of two positive integers a and b is the largest positive integer d that divides both a. 980 78 12 44. Discuss on euclids division lemma and related questions.

So x divides both 369 and 697. Extra Questions On Euclids Division Algorithm Euclids division algorithm is a technique to compute the Highest Common Factor HCF of two given positive integers. Let us consider a 217 b 5 be two integers.

All the questions are based on Euclids Division Lemma and its applications. I Consider number 23 and 5 then. In Exercise 11 of Class 10 Maths Chapter 1 there are only five questions.

78 44 1 34.

Euclid S Division Algorithm Solved Examples Numbers Cuemath