find the hcf of two numbers experimentally based on euclids division lemma by using colour strips. ( like an activity )
Answers
Answer:
To find the HCF of two numbers experimentally based on Euclid's division lemma.
Material Required
Square sheet and maths kit.
Procedure
1. Cut one strip of length “
a
” units (
a=11 cm
) and one strip of length “
b
” units (
b=8 cm
) of width 1 cm each (
a>b
).
2. Paste the strips of length “
a
” units above the strip of length “
b
” units aligning them from length as shown in fig 1. The remaining length is say
c cm
(
c=3 cm
,
b>c
).
3. Cut another strip of length
b
units and 2 strips of
c
units. Paste the strip of
b
units above the strips of
c
unit aligning them from left ad shown in fig 2. The remaining length is say
d
cm. (
d=2 cm
,
d<c
)
4. Repeat the process till the length proceeding strips covered completely and second strip which covers the proceeding strips is the HCF of given number (fig 4).
Observation
By Euclid's division lemma
a=bq+r
,
0≤r<b
Fig 1. Shows
a=b×1+c (q=1,r=c)
Fig 2. shows
b=c×2+d (q=2,r=d)
Fig 3. shows
c=d×1+e (q=1,r=e)
Fig 4. shows
d=e×2+0 (q=2,r=0)
H.C.F. of
a
and
b
is
e
.
Here,
a=11 cm
,
b=8 cm
,
c=3 cm
,
d=2 cm
and
e=1 cm
H.C.F of 11 and 8 is 1.
Conclusion
Euclid's division lemma can be used for finding the HCF of two or more numbers.