Question

If I=<24,36,42> be an ideal of a ring Z then find a such that I=<a>.

Answer 1

by properties of the Ideal:

$\forall a,b\in I\; a-b\in I$

Substitute all possible values and find their GCD:

$36-24=12\\ 42-24=18\\ 42-36=6\\ GCD=6$

From the fact that 24, 36, 42 are divided by 6, it follows $I=<6>$