Cal11 calculator
Search calculator...

Positive Factors Calculator

Reviewed by Calculator Editorial Team

A positive factor of a number is an integer that divides that number exactly without leaving a remainder. This calculator helps you find all positive factors of any integer you input.

What Are Positive Factors?

Positive factors, also known as divisors, are whole numbers that can be multiplied together to produce another number. For example, the positive factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 exactly.

Factors are fundamental in number theory and have practical applications in various fields including cryptography, computer science, and engineering.

How to Find Positive Factors

To find all positive factors of a number, follow these steps:

  1. Start with the number 1, which is always a factor of any number.
  2. Check each integer from 2 up to the square root of the number to see if it divides the number exactly.
  3. For each divisor found, its complement (the number divided by the divisor) is also a factor.
  4. List all unique factors found in this process.

Note: The square root is used as a stopping point because any factor larger than the square root would have a corresponding factor smaller than the square root.

Positive Factors Examples

Let's look at a few examples to understand how positive factors work:

Number Positive Factors
6 1, 2, 3, 6
15 1, 3, 5, 15
20 1, 2, 4, 5, 10, 20
28 1, 2, 4, 7, 14, 28

Positive Factors Formula

The process of finding positive factors can be summarized with this algorithm:

  1. Initialize an empty list to store factors.
  2. Add 1 to the list (since 1 is always a factor).
  3. For each integer i from 2 to √n:
    • If n is divisible by i, add both i and n/i to the list.
  4. Sort the list in ascending order.
  5. Remove any duplicate factors.
  6. Return the sorted list of unique factors.

Positive Factors Table

Here's a table showing positive factors for numbers 1 through 20:

Number Positive Factors
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
10 1, 2, 5, 10
11 1, 11
12 1, 2, 3, 4, 6, 12
13 1, 13
14 1, 2, 7, 14
15 1, 3, 5, 15
16 1, 2, 4, 8, 16
17 1, 17
18 1, 2, 3, 6, 9, 18
19 1, 19
20 1, 2, 4, 5, 10, 20

FAQ

What is the difference between factors and multiples?

Factors are numbers that divide another number exactly, while multiples are numbers that can be divided by another number exactly. For example, the factors of 6 are 1, 2, 3, and 6, while the multiples of 6 are 6, 12, 18, etc.

Can negative numbers have positive factors?

Yes, negative numbers can have positive factors. For example, the positive factors of -12 are the same as the positive factors of 12: 1, 2, 3, 4, 6, and 12.

How many factors does a prime number have?

A prime number has exactly two positive factors: 1 and itself. For example, the number 7 has factors 1 and 7.

What is the largest possible number of factors a number can have?

The number with the most factors is highly composite numbers. For example, 120 has 16 factors, which is more than any number below it.