Which of the following numbers are divisible by 8? i. 5240 ii. 5220 iii. 97128…

Concept

A whole number is divisible by 8 if and only if the number formed by its last three digits is divisible by 8. Since 1000 = 8 × 125, every place value to the left of the last three digits contributes a multiple of 8 and cannot change the divisibility result.

Application

1. For 5240, use 240: 240 ÷ 8 = 30 exactly, so 5240 is divisible by 8.

2. For 5220, use 220: 220 ÷ 8 = 27.5, which is not an integer, so 5220 is not divisible by 8.

3. For 97128, use 128: 128 ÷ 8 = 16 exactly, so 97128 is divisible by 8.

4. For 97124, use 124: 124 ÷ 8 = 15.5, which is not an integer, so 97124 is not divisible by 8.

Cross-check

Direct division gives 5240 ÷ 8 = 655 and 97128 ÷ 8 = 12141, both integers. The other two quotients are 652.5 and 12140.5, so the same classification is obtained.

Result

Therefore, 5240 and 97128—items i and iii—are the numbers divisible by 8.