Question

The number of distinct prime factors of the smallest 5-digit number is
(A) 2 (B) 4 (C) 6 (D) 8

Answer 1

The smallest 5 digit no is :10000.
By factorizing it and breaking down into prime factors we get:
2*2*2*2*5*5*5*5
Distinct prime factors are 2 and 5.
Number of distinct prime factors is (A) 2.

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Answer 2

Answer:

Option A - 2  

Step-by-step explanation:

To find : The number of distinct prime factors of the smallest 5-digit number ?

Solution :

The smallest five digit number is 10000.

We find the prime factor of 10000.

2 | 10000

2 | 50000

2 | 25000

2 | 12500

2 | 6250

5 | 3125

5 | 625

5 | 125

5 | 25

5 | 5

  | 1

$10000=2\times 2\times2\times 2\times2\times 5\times5\times 5\times5\times 5$

$10000=2^5\times5^5$

The distinct prime numbers are 2 and 5.

Therefore, option A is correct.