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 ✓)

÷4: the last two digits form a multiple of 4. ÷8: the last three digits form a multiple of 8.

Because 100 is divisible by 4 and 1000 by 8, every place above them vanishes from the remainder:

• ÷4: 11,564 → look at 64 → 64 ÷ 4 = 16 → divisible. ✓
• ÷8: 74,152 → look at 152 → 152 ÷ 8 = 19 → divisible. ✓

In general 2ⁿ divides 10ᵏ exactly when k ≥ n, so ÷2 needs 1 digit, ÷4 needs 2, ÷8 needs 3, ÷16 would need 4.