# Math Class 10

1
Euclid’s Division Lemma and Algorithm

In This Video We Learn Euclid's Division Theorem

Euclid's Division Theorem is combination of Euclid's Division Lemma and Euclid's Division Algorithm.

Euclid's Division Theorem State : for Given Positive Integer a and b. there exist unique integers q and r which satisfying the equation

a = q times b + r

where r is greater than and equal to 0 or smaller than b

Euclid's Division Algorithm: is a group or set of instruction which use to find the HCF of Two given positive integers.

it contain some steps which we have to follow to find the HCF of any two given positive integers.

To obtain the HCF of two positive integers, say c and d, with c is greater than d, follow

the steps below:

Step 1 Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and r such that c = d multiply q + r, r is greater or equal to 0 or smaller than b

Step 2 If r = 0, d is the HCF of c and d. 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.

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