Subscribe us: http://goo.gl/e3Ar9O
NCERT solutions Google plus page: https://plus.google.com/+Gyanpub/posts
Google Plus: https://plus.google.com/+phanicbse
Euclid’s division algorithm, as the name suggests, has to do with divisibility of
integers. Stated simply, it says any positive integer acan be divided by another positive
integer bin such a way that it leaves a remainder rthat is smaller than b. Many of you
probably recognise this as the usual long division process. Although this result is quite
easy to state and understand, it has many applications related to the divisibility properties
of integers. We touch upon a few of them, and use it mainly to compute the HCF of
two positive integers.
1.2 Euclid’s Division Lemma
Consider the following folk puzzle.
A trader was moving along a road selling eggs. An idler who didn’t have
much work to do, started to get the trader into a wordy duel. This grew into a
fight, he pulled the basket with eggs and dashed it on the floor. The eggs broke.
The trader requested the Panchayat to ask the idler to pay for the broken eggs.
The Panchayat asked the trader how many eggs were broken. He gave the
If counted in pairs, one will remain;
If counted in threes, two will remain;
If counted in fours, three will remain;
If counted in fives, four will remain;
If counted in sixes, five will remain;
If counted in sevens, nothing will remain;
My basket cannot accomodate more than 150 eggs.
An algorithmis a series of well defined steps
which gives a procedure for solving a type of
An equivalent version of Theorem 1.2 was probably first
recorded as Proposition 14 of Book IX in Euclid’s
Elements, before it came to be known as the Fundamental
Theorem of Arithmetic. However, the first correct proof
was given by Carl Friedrich Gauss in his Disquisitiones
Carl Friedrich Gauss is often referred to as the ‘Prince of
Mathematicians’ and is considered one of the three
greatest mathematicians of all time, along with Archimedes
and Newton. He has made fundamental contributions to
both mathematics and science.
The Fundamental Theorem of Arithmetic says that every composite number
can be factorised as a product of primes. Actually it says more. It says that given
any composite number it can be factorised as a product of prime numbers in a
‘unique’ way, except for the order in which the primes occur. That is, given any
composite number there is one and only one way to write it as a product of primes,
as long as we are not particular about the order in which the primes occur. So, for
example, we regard 2 × 3 × 5 × 7 as the same as 3 × 5 × 7 × 2, or any other
possible order in which these primes are written. This fact is also stated in the
The prime factorisation of a natural number is unique, except for the order
of its factors.
Tagged under: ncert class 9 solutions,ncert solutions,cbselabs,gyanpub,learncbse,ncert solutions class 9,ncert textbooks,ncert text book solutions,online material real numbers free,free ncert solutions,ncert,cbse,real numbers,common core math
Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.
Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip
Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans
1. Students enter a simple code
2. You play the video
3. The students comment
4. You review and reflect
* Whiteboard required for teacher-paced activities
With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.
Carry out a quickfire formative assessment to see what the whole class is thinking
Create interactive presentations to spark creativity in class
Student teams can create and share collaborative presentations from linked devices
Turn any public video into a live chat with questions and quizzes