6. By Euclid Division Lemma x=qy+r , x>y
the value of q and r for x=27 and y = 5
are?
a) q=5 r=2 b) cannot be determined
c) q = 6, R=3 d) q=5, r=3
Answers
Step-by-step explanation:
We all know that According to Euclid's Division algorithm,any two numbers x and y can be expressed as.
x=qy+r
x>y ----(given)
To find the value of x=27,y=5.
put the value in division algorithm,
27=q×5+r
27=5×5+2
so,
q=5
r=2.
.
The value of q and r are 5 and 2 respectively. hence the correct option is (a).
By Euclid Division Lemma, x = qy + r, x > y.
The value of q and r for x = 27 and y = 5 are :
- a) q = 5 , r = 2
- b) cannot be determined
- c) q = 6, r = 3
- d) q = 5, r = 3
Euclid division Lemma : If a number x is divided by y, the quotient will be q and remainder will be r then, x = qy + r, where 0 ≤ r < q.
Here, x = 27 and y = 5
∴ 27 = 5q + r
Now If we arrange 27 in the form of 5q + r we can get the answer easily. So let's do it.
⇒ 27 = 25 + 2 = 5 × 5 + 2
∵ 27 = 5q + r
∴ 27 = 5 × 5 + 2 = 5q + r
On comparing we get, q = 5 and r = 2.
Therefore the value of q and r are 5 and 2 respectively.
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