NCERT Solutions for Maths CBSE Class 10 Real Numbers Ex 1.1 q5
This video demonstrates how to find HCF using Euclid’s division lemma or Euclid’s division algorithm.Statement of Euclid’s division algorithm and its appliction to solve word problems is illustratedin detail.Generalised results are proven by Euclid’s division algorithm.
Euclid’s Division Lemma : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 = r is less than b.
A lemma is a proven statement used for proving another statement.
00:02 Q5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9 m, 9 m + 1 or 9m + 8.
00:38 Note down the values of a , b in Euclid’s division lemma.
01:10 use Euclid’s division lemma
01:45 consider the case for r=0
02:36 Take r=1
04:38 consider the case for r=3
Euclid’s division algorithm is a technique to compute the Highest Common Factor HCF of two given positive integers. Recall that the HCF of two positive integers a and b is the largest positive integer d that divides both a and b .
Euclid’s division algorithm
To find the HCF of two positive integers, say c and d, with c is greater than d, followthe steps below:
Step 1 : Apply Euclid’s division lemma, to c and d . So, we find whole numbers, q andr such that c = dq + r , 0 = r is less than d .
Step 2 : If r = 0, d is the HCF of c and d . If r not zero 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.
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