State Euclid's division lemma

What is the use of Euclid's division lemma ?

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 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 . (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 show that they can be rewritten in the form 3m or 3m + 1 .]

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 show that they can be rewritten in the form 3m or 3m+1].

By applying Euclid's division lemma, 72 and 28 can be expressed as :

17 = 6 xx2 +5 is compared with Euclid's Division lemma a = bq +r then which number is representing the remainder

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

(i) Use Euclid's division algorithm to find the HCF of: 135 and 225 (ii) Use Euclid's division algorithm to find the HCF of: 196 and 38220 (iii) Use Euclid's division algorithm to find the HCF of: 867 and 255,