state Euclid division lemma and algorithm
Answers
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.
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.