I personally have to have an even number. It drives my OCD crazy if I don't. I once put in a sell order that was partially filled. it left me with an odd number. So my next purchase corrected it. I like my shares evenly divisible by 100 at least.
To make a trade requires both a buyer and a seller, or very often multiple buyers and sellers.
Many times my bid to buy 10,000 share is only partially filled because ther e was one seller who had 6000 shares and another who had 343 shares left over from his ask. This is especially true if you are making limit bids or asks near the spread, trying to catch a bottom or a top.
I have had trades partially filled for 3465 shares in the morning and then 3005 shares later in the day, then completed with 3030 shares hours or days later. I bought 10,000 shares, but it shows on the time/sales charts as three odd amounts.