State Euclid Division lemma

State Euclid Division lemma.

Find the HCF (865, 255) using Euclid’s division lemma

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.

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 Euclids division Lemma to show that the cube of any positive integer is either of the form 9m ,\ 9m+1 or, 9m+8 for some integer m .

Use Euclids division Lemma to show that the cube of any positive integer is either of the form 9m ,\ 9m+1 or, 9m+8 for some integer m .

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. [Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and sho

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.[Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and sho

Using Euclid's division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.