# Prove that (integer)-(the sum of it's digits) can be divided by 9 [duplicate]

How to prove this:

1. Choose whichever integer you like
2. Subtract from it the sum of it's digits
3. The result can always be divided by 9

For example:

1. I choose 123.
2. The sum of it's digits is 1+2+3=6.
3. 123-6 = 117. And 117/9 = 13.

## marked as duplicate by Bill Dubuque number-theory StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 7 '15 at 15:07

• Try ls = {a, b, c, d, e, f} and FromDigits[ls] - Total[ls] // Expand and see if you can generalize. – b.gatessucks Feb 7 '15 at 13:35