This activity helps you to find HCF of two positive numbers. We first observe the
following instructions.
(i) Construct a rectangle whose length and breadth are the given numbers.
(ii) Try to fill the rectangle using small squares.
(iii) Try with 1×1 square; Try with 2×2 square; Try with 3 3 ´ square and so on.
(iv) The side of the largest square that can fill the whole rectangle without any
gap will be HCF of the given numbers.
(v) Find the HCF of (a) 12,20 (b) 16,24 (c) 11,9
Answers
Answer:
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Step-by-step explanation:
English is the predominant language and a de facto official language of New Zealand. Almost the entire population speak it either as native speakers or proficiently as a second language.[1] The New Zealand English dialect is most similar to Australian English in pronunciation, with some key differences. The Māori language of the indigenous Māori people was made the first de jure official language in 1987. New Zealand Sign Language (NZSL) has been an official language since 2006. Many other languages are used by New Zealand's minority ethnic communities.
Languages of New Zealand
Official
English (96.1%) Te reo Māori (3.7%)
New Zealand Sign Language
Answer:
Step-by-step explanation:
Aim
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.