Replace the symbols * and # in 9586*4# so that it is divisible by both 8 and 5.

Answer: * = 0, # = 0

Explanation:

Step 1 — divisibility by 5: The last digit must be 0 or 5, so # is either 0 or 5.

Step 2 — divisibility by 8: A number divisible by 8 must be even, so the last digit cannot be 5. Therefore # = 0.

Step 3 — now check the last three digits to test divisibility by 8. The last three digits are '*40'.

• If * = 0, last three digits = 040 which equals 40, and 40 ÷ 8 = 5, so it is divisible by 8.

• If * = 1, last three digits = 140 and 140 ÷ 8 = 17.5, so it is not divisible by 8.

Conclusion: The only pair that makes the number divisible by both 5 and 8 is * = 0 and # = 0.