So I'm sitting at the table the other day explaining factors to the primary-age little one, including some of the little "tricks" one can use to determine if a number is a factor, such as that if you add up all the digits of a multiple of 3, they will sum to 3, 6, or 9 (given enough iterations). A few minutes later, I ask, is 4 a factor of 72?

LO says "yes" immediately (even though LO does not have the multiplication facts memorized, and still does repeated addition to divide multi-digit numbers by 2). Surprised, I ask how LO knows this. Answer: the tens place is an odd number, and the ones place is a 2. I had to think about that for a minute.

I don't believe I had ever observed this, and, though math is not my personal strength, I am considered to be reasonably decent at math (I have a graduate degree in a STEM field). To top it off, the next child up quickly demonstrated that this is true for all whole numbers.