Home
Class 10
MATHS
Euclid's division Lemma states that for ...

Euclid's division Lemma states that for two positive integers a and b, there exist unique integers q and r such that `a=bq+r` where r must satisfy.

Text Solution

Verified by Experts

The correct Answer is:
`0 le r lt b`
Promotional Banner

Topper's Solved these Questions

  • REAL NUMBERS

    VK GLOBAL PUBLICATION|Exercise Proficiency Exercise (Long Answer Questions)|9 Videos
  • QUADRATIC EQUATIONS

    VK GLOBAL PUBLICATION|Exercise SELF-ASSESSMENT TEST|11 Videos
  • TRIANGLES

    VK GLOBAL PUBLICATION|Exercise SELF ASSESSMENT TEST|10 Videos

Similar Questions

Explore conceptually related problems

.For any positive integer a and 3 ,there exist unique integers q and r such that a=3q+r where r must satisfy:

Theorem 1.1 (Euclid’s Division Lemma) : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r leq b.

Prove that if a and b are integers with b>0, then there exist unique integers q and r satisfying a=qb+r, where 2b<=r<3b

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m ,9m+1 or 9m+8 .

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

The positive integers p,q and r, then possible value of r is 3(b)5(c)7(d)1

Show that the cube of a positive integer of the form 6q+r,q is an integer and r=0,1,2,3,4,5 is also of the form 6m+r