Sol.
Use Euclid’s division algorithm to find the HCF of :
Q.1
(i)
135
and
225
Since
225
>
135,
Applying Euclid’s Division Algorithm,
we get,
225
=
135
×
1
+
90
Now consider,
divisor 90
and
dividend 135
applying Euclid’s Division Algorithm,
we get,
135
=
90
×
1
+
45
Now consider,
divisor 45
and
dividend 90
applying Euclid’s Division Algorithm,
we get,
90
=
45
×
2
+
0
since remainder
=
0
∴
HCF (135, 225)
=
45
Dividend =
Divisor × Question + Reminder
)
225
135
135
-
90
1
) (
135
1
90
45
-
) (
90
2
90
-
0
Now, the divisor in this
division is required
HCF of 225 & 135
Exercise 1.1
Sol.
Use Euclid’s division algorithm to find the HCF of :
Q.1
(iii)
867
and
255
Since
867
>
255,
Applying Euclid’s Division Algorithm,
we get,
867
=
255
×
3
+
102
Now consider,
divisor 102
and
dividend 255
applying Euclid’s Division Algorithm,
we get,
255
=
102
×
2
+
51
Now consider,
divisor 51
and
dividend 102
applying Euclid’s Division Algorithm,
we get,
102
=
51
×
2
+
0
since remainder
=
0
∴
HCF (867, 255)
=
51
Divide, 867 by 255
Dividend =
Divisor × Question + Reminder
)
867
255
765
-
102
3
) (
255
2
204
51
-
) (
102
2
102
-
0
Now, the divisor in this
division is required
HCF of 867 & 255
Exercise 1.1