Question

What is Euclid's Division Lemma?

Answer 1

Euclid's Division Lemma:

• Euclid’s Division Lemma states that for any two given positive integers $a$ and $b$, there exist unique integers $q$ and $r$that satisfy the condition$a=bq+r,0\le r<b$.
• Euclid’s division lemma can be represented as$\mathrm{Dividend}=\left(\mathrm{Divisor}\times \mathrm{Quotient}\right)+\mathrm{Remainder}$.
• Euclid's Division Lemma is used to obtain the HCF of two positive integers.

Thus, Euclid’s Division Lemma states that for any two given positive integers$a$,$b$ there exist unique integers $q$, $r$that satisfy the condition

$\mathbf{a}\mathbf{=}\mathbf{bq}\mathbf{+}\mathbf{r}\mathbf{}\mathbf{,}\mathbf{}\mathbf{0}\mathbf{\le }\mathbf{r}\mathbf{<}\mathbf{b}$.