Answer :

By Euclid's algorithm

We know that Dividend = Divisor × Quotient + Remainder

⇒ 7344 = 1260 × 5 + 1044

⇒ 1260 = 1044 × 1 + 216

⇒ 1044 = 216 × 4 + 180

⇒ 216 = 180 × 1 + 36

⇒ 180 = 36 × 5 + 0

So, HCF of 1260 and 7344 is 36 because when the divisor is 36 remainder is 0.

**OR**

We know by Euclid's algorithm if a and b are two positive integers, there exist unique integers q and r satisfying,

a = bq + r where 0 ≤ r < b

Let, b = 4

a = 4q + r , 0 ≤ r < 4

So, r can be 0,1,2 and 3.

If r =0,

a = 4q

= 2(2q)

= 2n where n = 2q

which is an even integer.

If r =1,

a = 4q + 1

= 2(2q) + 1

= 2n + 1 where n = 2q

which is an odd integer.

If r =2,

a = 4q + 2

= 2(2q +1 )

= 2n where n = 2q + 1

which is an even integer

If r =3,

a = 4q + 3

= 4q + 2 + 1

= 2(2q +1) + 1

= 2n + 1 where n = 2q + 1

which is an odd integer

Thus "a" can be 4q, 4q + 1, 4q + 2, 4q + 3.

4q or 4q + 2 is not possible because they are even integers.

So, 4q + 1 or 4q + 3 are representing odd integers.

Hence, every positive odd integer is of the form (4q + 1) or (4q + 3).

Rate this question :