Comprehensive Calculator Guide
This calculator lists all the factors of a number, its factor pairs, how many there are and their sum, and classifies the number as perfect, deficient or abundant. 36 has 9 factors; the factors of 28 apart from itself add up to 28, so it is perfect.
Factor pairs
Factors come in pairs that multiply to the number, so search only up to its square root. Only perfect squares have an odd number of factors. Perfect numbers, such as 6, 28, 496 and 8128, equal the sum of their other factors.
How to Use
- Enter a positive whole number.
- Nothing else is needed.
- Press “List factors” to see the factors, count, sum and classification.
Formula Used
Each factor d pairs with n ÷ d
Practical Examples
- Example 1: 36
- 9 factors; abundant.
- Example 2: 28
- 6 factors; perfect.
- Example 3: 360
- 24 factors summing to 1,170.
Important Tips
- Search up to the square root.
- Use prime factors to count.
- 1 and n are always factors.
Common Mistakes to Avoid
- Leaving out 1 or n.
- Listing a square’s root twice.
- Confusing factors with multiples.
Frequently Asked Questions
- What are the factors of 24?
- 1, 2, 3, 4, 6, 8, 12, 24.
- Factor vs multiple?
- 3 is a factor of 12; 24 is a multiple of 12.
- What is a perfect number?
- One equal to the sum of its other factors, like 6.