Common Remainder

144 divided by n leaves a remainder of 11. 220 divided by n also leaves a remainder of 11. What is n?
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Problem



When $144$ is divided by $n$, this leaves a remainder of $11$. When $220$ is divided by $n$, this also leaves a remainder of $11$. What is the value of $n$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.