Download NCERT Solutions Class 10 Maths Chapter 1 Real Numbers exercise 1.4, 1.3, 1.2 & 1.1 in Hindi (English & हिंदी medium) in PDF form for UP Board (High School) Schools as well as CBSE Board Schools. These solutions and study material related to this chapter is modified according to latest CBSE Syllabus 2018-19. The fundamental theorem of arithmetic and Euclid’s division lemma are the main topics of this chapter (Real Numbers). The Fundamental Theorem of Arithmetic and Euclid’s division lemma has many applications, both within mathematics and in other fields. NCERT Solutions of all other subjects are also available in PDF format.
NCERT Solutions Class 10 Maths Chapter 1
NCERT Solutions – Real Numbers
English Medium Solutions
हिंदी माध्यम के हल
Download the practice test series with answers. Level 1 Test 1 contains basic questions for practicing the chapter Real Numbers. Most of the questions of Level 1 Test 2 are easy to understand and provides good practice. Answers of these test series will be uploaded in July-August 2018.
What is algorithm?
An algorithm is a series of well-defined steps which gives a procedure for solving a type of problem.
A lemma is a proven statement used for proving another statement.
Euclid’s Division Lemma
For the given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, r = 0 or 0 < r < b.
Example of Euclid’s division lemma
Prove that the square of an integer is of the form 9k or 3k + 1.
Fundamental Theorem of Arithmetic
Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. In other word, the prime factorisation of a natural number is unique, except for the order of its factors.
The word algorithm come from the name of the name of the 9th century Persian mathematician al-Khwarizmi. The word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabr w’al-muqabala.
An equivalent version of Fundamental theorem of Arithmetic 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 al-Khwarizmi.
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.