Here you will find NCERT Solution for class 10 Maths Chapter 1 Real Numbers Exercise 1.1
students who are in class 10 and studing NCERT Books can refer these solutions.
To do exercise 1.1 you have to understand some concept
1. Real Number- Real number includes all rational and irrational numbers. and we can plot any real number on a number line.
2. Euclid Division Lemma- Lemma means a proper statement used for proving another statement.
and Euclid division Lemma says that For each pair of given integers a and b, there exist unique whole number q and r which satisfies the relation
a = bq + r where 0 ≤ r < b where q and r can also be 0.
Here a is dividend and b is divisor, q is quotient and r is remainder.
So, dividend = (divisor ✕ quotient) + remainder
3. Euclid Division Algorithm- An algorithm is a series of well defined steps which gives a procedure for solving a type of problem.
as the name suggest has to do with divisibility of integers. which means that any positive integer a can divided by another integer b in such a way that it leaves a remainder r that is smaller than b.
Many people usually recognise it as a long division method but we use Euclid Division Algorithm to compute HCF of given two numbers.
to obtain the HCF of two positive integers say a and b with a > b follow these steps
Step 1: Apply Euclid's division lemma to a and b. so, we find whole numbers q and r such that a = bq + r where 0 ≤ r < b.
Step 2: If r = 0, then b is the HCF of a and b. If r ≠ 0, apply the division lemma to d and r.
Step 3 : Continue the process till the remainder is zero. the divisor at this stage will be the required HCF.
Now you can easily understand the exercise 1.1 (real numbers)
Question 1:
Use Euclid's division algorithm to find the HCF of
1. 135 and 225
2. 196 and 38220
3. 867 and 255
Solution:
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