What least value must be assigned to * so that the number 63576*2 is divisible…

Concept: A number is divisible by 8 if and only if the 3-digit number formed by its last three digits is divisible by 8, because 1000 = 8 × 125, so any digits beyond the last three represent a multiple of 1000 and hence a multiple of 8.

Working: The number is 63576*2, so its last three digits form 6*2, i.e. 602 + 10×(*). Check each digit from 0 upward:

1. * = 0 → last three digits = 602; 602 ÷ 8 = 75 remainder 2 — not divisible.

2. * = 1 → last three digits = 612; 612 ÷ 8 = 76 remainder 4 — not divisible.

3. * = 2 → last three digits = 622; 622 ÷ 8 = 77 remainder 6 — not divisible.

4. * = 3 → last three digits = 632; 632 ÷ 8 = 79 remainder 0 — divisible.

Since * = 3 is the smallest digit for which the last three digits become divisible by 8, it is the least value required (checking the remaining digits shows only * = 7 also works, giving 672, but 3 is smaller).

Cross-check: 632 = 600 + 32 = (8 × 75) + (8 × 4) = 8 × 79, confirming 632 is exactly divisible by 8 with no remainder.

Answer: The least value that must be assigned to * is 3.