Test of Divisibility : Number Properties

The question is a Number Systems and number theory question on test of divisibility.

Question

10²⁵ - 7 is divisible by

1. 2
2. 3
3. 9
4. Both (2) and (3)

Correct Answer - 3. Choice (2)

Explanatory Answer

To find the number of factors of a given number, express the number as a product of powers of prime numbers.

10²⁵ - 7 = (10²⁵ - 1) - 6

The number 10²⁵ - 1 = 99.....9 (25 digits) is divisible by 3.

Therefore, (10²⁵ - 1) - 6 = (24 nines and unit digit is 3) 99.......93.

This number is divisible by 3 (from amongst the given choices).

Correct answer choice (2)

Level of difficulty : Moderate

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