Factor calculator
List the positive factors of an integer and check whether it is prime.
What this calculator covers
Use this factor calculator to list every positive divisor of an integer and see the matching factor pairs.
It is useful for quick number-theory checks, prime detection, and sanity-checking fraction or polynomial work that depends on clean divisibility.
Frequently asked questions
- What is the difference between a factor and a multiple?
- A factor of n divides n exactly with no remainder, while a multiple of n is n multiplied by some integer. For example, 3 is a factor of 12, and 24 is a multiple of 12. This calculator finds factors, not multiples.
- How does the calculator determine whether a number is prime?
- A number is prime if its only positive divisors are 1 and itself — meaning the factor list has exactly two entries. The calculator checks all divisors up to the square root of the input, so if none divide cleanly except 1 and the number itself, it is flagged as prime.
- Why can I only enter positive integers?
- Factors are conventionally defined for positive integers. Negative numbers and non-integers introduce sign and non-integer divisibility complications that are outside the scope of standard factor listing. The calculator accepts values from 1 through 1,000,000,000.
- What are factor pairs and how do I read them?
- Factor pairs list each divisor alongside its complementary partner: two numbers that multiply together to give the original value. For 12, the pairs are 1×12, 2×6, and 3×4. Pairs are useful for quickly spotting factoring options in algebra problems or simplifying fractions.
Tool
Run the calculation
Result
RESULT · FACTORS
â„–211
Primary result
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The positive factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. That makes 12 total factors.
- Factors
- 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Factor pairs
- 1 x 84 · 2 x 42 · 3 x 28 · 4 x 21 · 6 x 14 · 7 x 12
- Factor count
- 12
- Prime
- No
Step-by-step solution
- 1.Test divisors from 1 through sqrt(84) to find every whole number that divides 84 with remainder 0.
- 2.For each divisor, pair it with 84 divided by that divisor to capture the matching large factor.
- 3.Sort the complete list in ascending order to get 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Walkthrough
Visual walkthrough
Factor searches only need to scan up to the square root because every small divisor automatically reveals its matching large partner.
01
Check the divisor range
1 through sqrt(84)
Any divisor larger than the square root is paired with one already found below that point.
02
Build the factor pairs
1 x 84 · 2 x 42 · 3 x 28 · 4 x 21 · 6 x 14 · 7 x 12
Each clean division gives one low factor and one matching high factor.
03
Read the ordered factor list
After the pairs are merged and sorted, the result is the full set of positive factors.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84