The least value that must be given to the digit aaa so that the number 91876a2 is divisible by 8 is 3.

Explanation:

A number is divisible by 8 if its last three digits form a number divisible by 8. Here, the last three digits are "6a2", which can be expressed as:

600+10a+2=602+10a600+10a+2=602+10a600+10a+2=602+10a

Since 600 is divisible by 8, the divisibility depends on 10a+210a+210a+2 being divisible by 8. Testing values for aaa (0 to 9):

• For a=3a=3a=3, 10×3+2=3210\times 3+2=3210×3+2=32, which is divisible by 8.

Thus, the smallest such value of aaa is 3