number of starting hands

I often see books say that there are only 169 starting hands for texas hold em. Can somebody explain the math of that to me? I know it's 13x13, but that doesn't seem quite right to me, because that doesn't take into account the possibility of suiting your hand.

For example...think of 2 through A of two suits, say hearts and spades(inconsequential which suits we choose, because the hand can either be suited(A [img]/images/graemlins/heart.gif[/img], K [img]/images/graemlins/heart.gif[/img]) or unsuited A [img]/images/graemlins/heart.gif[/img], K [img]/images/graemlins/spade.gif[/img], [img]/images/graemlins/diamond.gif[/img], [img]/images/graemlins/club.gif[/img] s are all the same). The A [img]/images/graemlins/heart.gif[/img] could be paired with 2 [img]/images/graemlins/spade.gif[/img] through A [img]/images/graemlins/spade.gif[/img], and also the 12 other [img]/images/graemlins/heart.gif[/img] cards, for a possible 25 hands. Now go to the K [img]/images/graemlins/heart.gif[/img], it could pair with any of the spades and any of the 11 other heart cards(it already paired with the ace) for 24 possible hands....and so on with the Q [img]/images/graemlins/heart.gif[/img], J [img]/images/graemlins/heart.gif[/img], etc. So the equation becomes 25(A)+24(K)+23(Q)+22(J)+.....14(3)+13(2)= 247 The number in the parentheses is the heart card, preceded by the possible combination of cards remaining for that card.

So is it 169 starting hands or 247?