7 is the largest single-digit prime, so its products share no tidy digit pattern with friendlier tables.
Multiples of 5 always end in 0 or 5. The digits of every multiple of 9 add up to 9. But 7's multiples (7, 14, 21, 28, 35, 42, 49, 56, 63) give your eye nothing obvious to grab. With no shape to lean on, most people fall back on raw memory, which is exactly why these facts slip away fastest.