Shortcut Trick
A number is exactly divisible by 8 if its last three digits are divisible by 8 or are 000.
Checking last 3 digits: 52832 ⇒ 832 ÷ 8 = 104 (Rem. = 0) → Divisible
Checking last 3 digits: 85332 ⇒ 332 ÷ 8 = 41.5 (Rem. = 4) → Not Divisible
Checking last 3 digits: 58332 ⇒ 332 ÷ 8 = 41.5 (Rem. = 4) → Not Divisible
Checking last 3 digits: 82532 ⇒ 532 ÷ 8 = 66.5 (Rem. = 4) → Not Divisible
∴ The correct answer is 52832.
Alternate Method
Given Numbers: 52832, 85332, 58332, 82532
Concept Used: To check divisibility by 8, we focus only on the hundreds, tens, and units place digits of the given number.
Step-by-Step Calculation:
⇒ For 52832: Last three digits are 832. Since 8 × 100 + 8 × 4 = 800 + 32 = 832, it is divisible.
⇒ For 85332: Last three digits are 332. 332 ÷ 8 ⇒ 320 is divisible, but 12 is not. Remainder = 4.
⇒ For 58332: Last three digits are 332. Remainder = 4. Not divisible.
⇒ For 82532: Last three digits are 532. 532 ÷ 8 ⇒ 480 is divisible, leaving 52. 52 ÷ 8 leaves Remainder = 4.
Since only 52832 leaves a remainder of 0 when the last 3 digits are divided by 8, the entire number is divisible by 8.
∴ The correct answer is 52832.
Additional Information
Divisibility by powers of 2
A number is divisible by 2n if its last n digits are divisible by 2n. For example, 4 (22) requires the last 2 digits, and 16 (24) requires the last 4 digits.
Divisibility by 8 (Shortcut for Hundreds Digit)
If the hundreds digit is even (0, 2, 4, 6, 8), check if the last two digits are divisible by 8. If the hundreds digit is odd (1, 3, 5, 7, 9), add 4 to the last two digits and check if the result is divisible by 8.
Divisibility by 3 and 9
A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.