Variable confusion in Euclid division lemma

Question

For given positive integer 10 and 3 which of the following is correct according to Euclid division lemma?
(a.) $10=3×3+1$
(b.) $3=10×0+3$ Please explain it.

( I am a 10th grade student.)

(Feel free to edit tag if given one is not suitable)

Answer 1

Both of the statements are correct; in fact the Euclid lemma says:

Let $a,b \in Z$ and $b\neq0$. There exist only a couple of integers, $r\in Z$ and $q \in N\cup\left \{ 0 \right.\left.\right\}$such that: $$\left\{\begin{matrix} a=b\cdot q+r \\ 0\leq r < |b| \end{matrix}\right.$$

In both cases the two conditions are satisfied so both statements are true.