How many positive factors of 12 are there?

Appeared in: CIP Ranchi 2023

Explanation

A factor of a number is an integer that divides it completely without leaving a remainder.
The positive factors of 12 can be found by listing pairs of numbers that multiply to 12: (1, 12), (2, 6), and (3, 4).
Listing these unique numbers gives: 1, 2, 3, 4, 6, 12.
Counting these factors shows there are a total of 6.

Option A: The number 2 is an incorrect count. While 2 is a factor of 12, there are several other factors (1, 3, 4, 6, 12).
Option C: The number 10 is an incorrect count. 12 has only 6 factors.
Option D: The number 8 is an incorrect count. 12 has only 6 factors.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the basic mathematical concept of finding the number of positive factors of an integer as background academic context rather than a clinical decision trigger.
This is a non-clinical, general aptitude question.
Basic numeracy is a foundational skill for nurses, essential for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting lab results.
Strong mathematical skills help prevent errors and ensure patient safety in clinical practice.

How to Approach the Question

First, understand the question. It asks for the 'number' of 'positive factors' of 12.
Recall the definition of a 'factor': a number that divides another number evenly.
Method 1 (Listing): Systematically find all the numbers that divide 12. Start with 1 (1 × 12), then 2 (2 × 6), then 3 (3 × 4).
List all the unique numbers you found: 1, 2, 3, 4, 6, 12.
Count the numbers in your list. The total is 6.
Method 2 (Prime Factorization): Find the prime factors of 12 (12 = 22 × 31). Add 1 to each exponent (2+1=3, 1+1=2). Multiply the results (3 × 2 = 6).

Concept Tested & Keywords

Concept Tested: This question tests the basic mathematical concept of finding the number of positive factors of an integer.
Stem keywords: positive factors, 12
Lead-in keywords: How many

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