Contents
- ๐ What is this?
- ๐จ๐ปโ๐ป How to use it?
- ๐ฐ Examples
- ๐ Nuances
- ๐ค Frequently asked questions
- ๐ Related materials
How the divisor calculator works
A positive divisor divides a whole number without leaving a remainder. Enter a number and the calculator counts its positive divisors, adds them, and shows the ordered list on request.
Reading the count and sum
For 12, the divisors are 1, 2, 3, 4, 6 and 12. The count is six; the sum is 28. Both 1 and the number itself always belong to the list. A count of two means the number is prime, provided it is greater than one.
The first expression counts each positive divisor once. The second adds their values. The symbols describe different properties, so a large divisor sum does not imply a large divisor count.
The search pairs a small divisor with the number divided by it. At the square root of a perfect square, both members of the pair are the same and are included only once.
Checks worth trying
Enter 1. The only positive divisor is 1, so the count and sum are both 1. This is why one is not prime.
Enter 13. The list is 1 and 13. A count of two identifies this number as prime, and their sum is 14.
Enter 36. The nine divisors are 1, 2, 3, 4, 6, 9, 12, 18 and 36; their sum is 91. The unpaired central divisor 6 makes the count odd.
Enter 360. The count rises to 24 and the sum to 1,170. Opening the list is useful when choosing an exact group size or rectangular grid.
Input limits and common slips
Use a positive integer from 1 through 1,000,000,000,000. Zero has infinitely many positive divisors, so it cannot have a finite list here. Decimal and negative inputs are outside the tool's definition. Spaces grouping thousands do not change the number.
Dividing a number by a candidate and getting a nonzero remainder means it is not a divisor. For a square such as 49, do not count 7 twice. The calculation uses integers, so the displayed count and sum are exact.
Questions about divisors
These boundary cases also provide quick ways to check the result by hand.
Does every positive integer divide itself?
Yes. Dividing n by n gives 1 with no remainder, so n is always the final positive divisor.
Is one included in every list?
Yes. Any positive integer divided by 1 leaves no remainder.
Why can a square have an odd divisor count?
Its square-root divisor pairs with itself. All other divisors form two distinct members of a pair.
Do you include negative divisors?
No. The list and the divisor functions shown here use only positive divisors.
What is the sum of divisors of a prime p?
It is p + 1, since the only positive divisors are 1 and p.
Similar calculators
You may find the following calculators on the same topic useful:
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- Median absolute deviation calculator. Enter numbers to find the typical distance from their median.
- Fraction to decimal calculator. Enter a numerator and denominator to see the decimal value; add a whole part if needed.
- Coefficient of variation calculator. Enter a list of numbers to see their relative spread as a percentage.
- Variance calculator. Paste numbers, choose a data type, and see how far the values spread around their mean.
- Simple Calculator. Simply calculate whatever you need.
- Pi Calculator. Find out the value of Pi with the desired number of decimal places.
- Calculator for the Number 'e'. Calculate the desired number of decimal places in the number 'e' (Euler's number or Napier's constant) using the 'e' number calculator.
- Quadratic Equations Calculator. Apply methods to solve quadratic equations using formulas, discriminant, and Vieta's theorem.
- Percentage Less Calculator. Calculate online how much one number is less than another in percentage.
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