Which of the following numbers will completely divide (729 - 730 - 731 + 732) ?
2021
Which of the following numbers will completely divide (729 - 730 - 731 + 732) ?
- A.
26
- B.
51
- C.
72
- D.
78
Attempted by 60 students.
Show answer & explanation
Correct answer: C
Given Expression: 7^29 - 7^30 - 7^31 + 7^32
Factor out the smallest power (7^29):
7^29 * (1 - 7^1 - 7^2 + 7^3)
Simplify inside the brackets:
7^29 * (1 - 7 - 49 + 343)
7^29 * (344 - 56) = 7^29 * 288
Check Divisibility:
We need to check which option divides 7^29 * 288.
Checking Option 3 (72): Since 288 = 72 * 4, the expression is divisible by 72.
Final Answer: Option 3 (72)