modulo arithmetic help pls :>

[graceful wind]

Basically, I’m not too sure how to use properties of modulus to find the common divisor of three numbers that also share the same remainder (divisor>1 obv). Numbers (dividend) are 618, 343, and 277. Thank u!!

[round pewter]

Here I only give the hint of $618$ and $343$. Three integers can be generalized in similar ways: \
$\begin{cases} 618 \equiv r (mod ; d) \ 343 \equiv r (mod ; d) \end{cases}$ \
$618 \equiv 343 (mod ; d)$ \
$0 \equiv 275 (mod ; d)$ \
$\therefore \exists x \in \mathbb{Z}: 275 = dx$ \
Prime factorization of $275$: $5^2 \cdot 11$ \
$\therefore \min {d} = 5$

[neat drift]

Kelvin Chan (Tag me 2 reply)

[graceful wind]

Where would the 277 go into this?

Never mind I understand what u did now, thank u!!