This factor calculator lists every positive divisor of a whole number. Enter n. The default n = 60 returns 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Homework factor trees and divisibility checks start here. To combine two numbers into one shared greatest factor, use the GCF calculator.
How the formula works
Test each integer i from 1 to n. If n divided by i has no remainder, i is a factor. Collect all such i in ascending order.
Worked example
n = 60. Divisors include pairs (1,60), (2,30), (3,20), (4,15), (5,12), (6,10). Listed together they match the default result string.
| Input | Value |
|---|---|
| Number n | 60 |
| Factors | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 |
How to use the fields
- Number n is the positive integer to factor.
Factor pairs
Factors come in pairs that multiply to n. Listing pairs helps catch missing entries: if 5 is present, 12 must be present for 60.
Common mistakes
- Stopping after prime factors and forgetting composite divisors
- Omitting 1 or n
- Including numbers that do not divide evenly
- Confusing factors with multiples
Primes and composites
Prime n yields exactly two factors. Composite n yields more. Perfect squares have an odd count of positive factors because one factor is repeated in a pair.
Classroom practice
Students should find pairs on paper for 60, then compare to the calculator list. Mismatches usually mean a missed pair near the square root.
Next try a prime like 17 to see the short list 1, 17, while keeping site defaults documented as n = 60.
Word problems
Factors answer “how can I split n items into equal groups?” Each factor is a possible group size that divides evenly.
Multiples answer a different question about repeated addition of n.
Link to GCF and LCM
Shared factors of two lists lead to GCF. LCM problems often start from prime factorization instead of the full divisor list, but scanning factors still builds number sense.
Use the dedicated GCF page when you only need the greatest shared divisor.
Square root cutoff
You only need to test up to the square root when listing pairs by hand. Each small factor pairs with n divided by that factor. The calculator checks through n for clarity and returns the full ascending list.
Knowing the pair method still helps you spot a missing divisor in a handwritten list.
Factors versus multiples
Factors of 60 divide 60. Multiples of 60 are 60, 120, 180, and so on. Mixing those words is one of the most common homework language errors.
Ask “does it divide evenly into n?” when you mean factor.
Using the list with GCF
List factors of two numbers and highlight overlaps. The largest overlap is the GCF. For speed, the GCF calculator is better, but the visual overlap teaches the meaning.
For 60 and 48, shared factors include 1, 2, 3, 4, 6, and 12, so GCF is 12 when both numbers are in play.
Even and odd patterns
Even n always includes 2 as a factor. Odd n never does. Perfect squares show a middle factor equal to the square root. Spotting those patterns before you read the full list makes missing entries easier to notice.
For 60, the pairs around the square root sit near 7.75, so 6 pairs with 10 and 5 pairs with 12.
Classroom speed round
Give students 60 seconds to list factors of 60, then reveal the calculator list. Discuss which pair they skipped most often. Speed plus feedback beats copying a list without thinking.
Keep n = 60 as the shared default whenever you screenshot the tool for a lesson plan.
After the list appears, pick one factor at random and multiply it by its pair to confirm you land back on 60. That spot check makes the meaning of factor concrete for learners who only memorized the word.
Limitations
One positive integer per run. No prime factorization formatting, no negative divisors, and no algebraic factoring of expressions.