Examples to solve under euclids division lemma
Answers
(a) 20, 8
Let 20 = a and 8 = b
Therefore, by applying the relation
a
=
b
q
+
r
a=bq+r, where
0
≤
r
<
b
0≤r<b we get
20
=
8
×
2
+
4
20=8×2+4 (In this
q
=
2
q=2 and
r
=
4
r=4)
(b) 17, 5
Let 17 = a and 5 = b
Therefore, by applying the relation
a
=
b
q
+
r
a=bq+r, where
0
≤
r
<
b
0≤r<b we get
17
=
5
×
3
+
2
17=5×3+2 (In this
q
=
3
q=3 and
r
=
2
r=2
Exercise 1.1(NCERT Book)
Question - 1: Use Euclid’s division algorithm to find the HCF of:
(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
Solution: (i) 135 and 225
In the given problem, let 225 = a, and 135 = b
Therefore, by applying the relation
a
=
b
q
+
r
a=bq+r, where
0
≤
r
<
b
0≤r<b we get
225
=
135
×
1
+
90
225=135×1+90 (Here
r
=
90
r=90)
Since, r (remainder) is not equal to zero (0). Thus, by applying the Euclid’s division algorithm, by taking 135 = a, and 90 = b we get
135
=
90
×
2
+
45
135=90×2+45 (Here
r
=
45
r=45)
Since, in this step also, r is not equal to zero(0). Thus by continuing the Euclid’s division algorithm, by taking this time, 90 = a, and 45 = b we get
90
=
45
×
2
+
0
90=45×2+0 (In this step we get
r
=
0
r=0)
Therefore, 45 is the HCF of given pair 225 and 135
Thus, Answer: 45
Answer:
answer is in attachment
