PROPER FACTOR

Proper Factor

Definition Of Proper Factor

All the factors of a number except 1 and the number itself are called the Proper Factors of that number.

More About Proper Factor

Factor of a number is same as that of its divisor, but in case of proper divisor we include 1 also.

Video Examples: MATH LESSON: Finding Factors of a Number

Example of Proper Factor

The factors of 16 are 1, 2, 4, 8, and 16. The factors 2, 4, 8 excluding 1 and 16 are called the proper factors of 16.

Solved Example on Proper Factor

Ques: Identify the proper factors of 36.

Choices:

A. 2, 3, 4, 6, 9, 12, 18
B. 1, 2, 3, 4, 6, 9, 12, 36
C. 2, 3, 4, 6, 9, 12, 36
D. 2, 3, 4, 6, 8, 9, 12, 18
Correct Answer: A

Solution:

Step 1: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: Proper factors of 36 are 2, 3, 4, 6, 9, 12, and 18. [Exclude the factors 1 and itself.]

Quick Summary

Proper factors are factors of a number, excluding 1 and the number itself.
Proper factors are useful in determining if a number is deficient, abundant, or perfect.

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🍎 Teacher Insights

Emphasize the exclusion of 1 and the number itself when defining proper factors. Use visual aids, such as factor trees, to identify all factors before excluding the improper ones.

🎓 Prerequisites

Factors
Divisibility

Check Your Knowledge

Q1: What are the proper factors of 12?

1, 2, 3, 4, 6, 12 2, 3, 4, 6 1, 2, 3, 4, 6 3, 4

Q2: Which of the following is NOT a proper factor of 24?

2 3 24 4

Frequently Asked Questions

Q: What is the difference between a factor and a proper factor?
A: A factor of a number includes 1 and the number itself, while a proper factor excludes these two.

Q: Does every number have proper factors?
A: No, prime numbers only have 1 and themselves as factors, so they have no proper factors.