Question

state Euclid division lemma and algorithm

Answer 1

Answer:

If we have any two positive integers let say "x" and "y". Then we can find 2 whole number "r" and "s" such that x = y × r + s where 0 ≤ s < y.

Euclid's division lemma helps to identify the highest common factor of any two positive integers also it helps to show the common properties of positive integers.

Step-by-step explanation:

Consider the provided information.

According to Euclid’s division lemma:

If we have any two positive integers let say "x" and "y". Then we can find 2 whole number "r" and "s" such that x = y × r + s where 0 ≤ s < y.

For example:

Let say the numbers are 13 and 6.

Then 13 = 6 × 2 + 1

Here, x is 13, y is 6, r is 2 and s is 1.

Now, we can see that 0 ≤ s < y because 0 ≤ 1 < 6

Euclid's division lemma helps to identify the highest common factor of any two positive integers also it helps to show the common properties of positive integers.

Answer 2

According to Euclid's Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b. The basis of the Euclidean division algorithm is Euclid's division lemma.