For any two positive integers a and b, such that a > b. There exi… - Vidyadip

MCQ

For any two positive integers $a$ and $b,$ such that $a > b$. There exist $($unique$)$ whole numbers $q$ and $r$ such that:

A
$\text{a}=\text{qbr}$
B
$\text{b}=\text{aq}+\text{r},0\leq\text{r}<\text{b}$
✓
$\text{a}=\text{bq}+\text{r},0\leq\text{r}<\text{b}$
D
$\text{q}=\text{ar}+\text{b},0\leq\text{r}<\text{b}$

✓

Answer

Correct option: C.

$\text{a}=\text{bq}+\text{r},0\leq\text{r}<\text{b}$

Euclid’s Division Lemma states that for given positive integer $a$ and $b,$
There exist unique integers $q$ and $r$ satisfying a $=\text{bq}+\text{r},0\leq\text{r}<\text{b}$

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