QUESTION

CSAT

Medium

Maths

Prelims 2025

A question is given followed by two Statements 1 and 2. Consider the Question and the Statements and mark the correct option.

Question: What is the smallest 1-digit number having exactly 4 distinct factors?

Statement-1: 22 is one of the factors. Statement-2: 33 is one of the factors.

Which one of the following is correct in respect of the above Question and the Statements?

Select an option to attempt

Explanation

Step 1: Understand the question We need the smallest 1-digit number that has exactly 4 distinct factors.

Step 2: Analyze 1-digit numbers (1 to 9)

The number of factors of a number N=(a1+1)(a2+1)...N = (a_1+1)(a_2+1)... where N=p1a1×p2a2×...N = p_1^{a_1} \times p_2^{a_2} \times ...

NumberFactors
1{1}
2{1, 2}
3{1, 3}
4{1, 2, 4}
5{1, 5}
6{1, 2, 3, 6}
7{1, 7}
8{1, 2, 4, 8}
9{1, 3, 9}

Step 3: Identify number(s) with 4 factors → 6 and 8 both have 4 factors.

Step 4: Pick the smallest 1-digit such number → 6 (since 6 < 8).

Step 5: Check if we needed the statements We could find the answer (6) directly without any use of Statement 1 or 2.

Hence, the correct option is: (D) The question can be answered even without using any of the statements.

Trusted by 2L aspirants

Practice UPSC Prelims PYQs Smarter

Practice Now
  • Track accuracy & weak areas
  • See past trends & repeated themes
Start Practicing Now

Crack UPSC with your
Personal AI Mentor

An AI-powered ecosystem to learn, practice, and evaluate with discipline

SuperKalam is your personal mentor for UPSC preparation, guiding you at every step of the exam journey.

Download the App

Get it on Google PlayDownload on the App Store
Follow us

ⓒ Snapstack Technologies Private Limited