What are the divisibility rules for 2, 5, and 10, and why are they so simple?

Only the last digit matters: even → ÷2, ends 0 or 5 → ÷5, ends 0 → ÷10.

Every place value above the units is a multiple of 10, and 10 is divisible by 2, 5 and 10 — so all those higher places contribute nothing to the remainder. Only the units digit is left to decide it:

• ÷2: last digit is 0,2,4,6,8. (734 ✓)
• ÷5: last digit is 0 or 5. (615 ✓)
• ÷10: last digit is 0. (980 ✓)