Question : Which of the following numbers will completely divide 412 + 413 + 414 + 415?
Option 1: 3
Option 2: 7
Option 3: 11
Option 4: 17
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Correct Answer: 17
Solution :
Given:
4
12
+ 4
13
+ 4
14
+ 4
15
= 4
12
(1 + 4 + 4
2
+ 4
3
)
= 4
12
(1 + 4 + 16 + 64)
= 4
12
(85)
Since 85 has factors of 5 and 17.
$\therefore$ It is divisible by 17.
Hence, the correct answer is 17.
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