# Test of Divisibility : Number Properties

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

#### Question

10

^{25} - 7 is divisible by

- 2
- 3
- 9
- 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.

10

^{25} - 7 = (10

^{25} - 1) - 6

The number 10

^{25} - 1 = 99.....9 (25 digits) is divisible by 3.

Therefore, (10

^{25} - 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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