NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice QuestionsQuestion 28
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice Questions
Question. 28
The number of distinct prime factors of the smallest 5-digit number is
(A)
2
(B)
4
(C)
6
(D)
8
Detailed Answer with Explanation:
Step 1: The smallest 5-digit number is 10000.
Step 2: Write it using powers of 10: \(10000 = 10^4\).
Step 3: Factor 10 into primes: \(10 = 2 \times 5\).
Step 4: Substitute into \(10^4\): \(10^4 = (2 \times 5)^4\).
Step 5: Expand the power: \((2 \times 5)^4 = 2^4 \times 5^4\).
Step 6: The prime factors here are 2 and 5. They are different, so they are distinct.
Therefore, the number of distinct prime factors = 2.