Question

Find the integers between 100 and 999 that are divisible by 3 or 4.

a) 216
b) 312
c) 448
d) All of the above

Answer 1

All the provided integers 216, 312, and 448 are divisible by either 3 or 4, so the answer is 'All of the above'.

Step-by-step explanation:

To find the integers between 100 and 999 that are divisible by 3 or 4, each number provided in the question should be tested against divisibility rules for 3 and 4.

For a number to be divisible by 3, the sum of its digits must be divisible by 3. To be divisible by 4, the number's last two digits should be divisible by 4. Now, we will apply these rules to the numbers provided:

• 216 is divisible by 3 (2+1+6=9, which is divisible by 3) and also by 4 (since 16 is divisible by 4).
• 312 is divisible by 3 (3+1+2=6, which is divisible by 3) but not by 4 (since 12 is divisible by 4).
• 448 is divisible by 4 (since 48 is divisible by 4) but not by 3 (4+4+8=16, which is not divisible by 3).

Therefore, all the given integers a) 216 b) 312 c) 448 are correct since they are each divisible by either 3 or 4.