Teresa Manning

## Answered question

2023-02-28

In Euclid's Division Lemma when $a=bq+r$ where $a,b$ are positive integers then what values $r$ can take?

### Answer & Explanation

gelo1368m6

Beginner2023-03-01Added 5 answers

Find the integer's value.
According to Euclid's Division Lemma if we have two integers $a$ and $b$ then there exist unique integer $q$ and $r$ which satisfy the condition $a=bq+r$ where $0\le r
$r$ is the remainder and $b$ is the divisor and remainder is always less than divisor and greater than equal; to $0$
Example: $a=59$ and $b=5$
After according to Euclid's division lemma $a$ can be stated as
$a=bq+r⇒59=11·5+4$
then take $a=60$ and $b=5$
$a=bq+r⇒60=12·5+0$
We can see value of $r$ ranges from $0$ to less than $b$
Thus the value of $r$ is $0\le r

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