Find all factors of a number, count them, calculate their sum, and discover the prime factorization.
Factors
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Number of Factors12
Sum of Factors168
Prime Factorization2^2 × 3 × 5
Is Prime?No
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What is the Factor Calculator?
A factor (or divisor) of a number is any whole number that divides it evenly with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 without leaving a remainder. Prime factorization breaks a number into its prime number building blocks.
How it works
Enter a positive whole number. The calculator finds all numbers that divide it evenly, lists them in order, counts them, adds them up, and expresses the number as a product of prime numbers (its prime factorization). It also tells you whether the number itself is prime.
Factors of n = all integers d where n ÷ d has remainder 0. Prime factorization expresses n as p₁^a × p₂^b × ... where p are primes.
A factor divides a number with no remainder. Prime factorization rewrites the number as a product of prime powers, showing its atomic structure in terms of indivisible primes.
Examples
Input
Result
Notes
60
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
60 has 12 factors; their sum is 168; prime factorization is 2² × 3 × 5
36
1, 2, 3, 4, 6, 9, 12, 18, 36
A perfect square with 9 factors; 36 = 2² × 3²
17
1, 17
A prime number with only 2 factors (1 and itself)
How to use the Factor Calculator
Enter a positive whole number in the input field
The calculator instantly displays all factors in ascending order
Review the count of factors and their sum in the stats section
Check the prime factorization to see the number's atomic building blocks
Use the 'Is Prime?' stat to determine if the number has exactly 2 factors
Benefits
Saves time — find all factors without manual checking or trial division
Accurate prime factorization — decompose numbers into primes instantly
Educational — understand divisibility, prime numbers, and number structure
No guessing — comprehensive list ensures you don't miss a single factor
Free and anonymous — client-side tool with no accounts or tracking
Tips & common mistakes
Common mistakes
Forgetting that 1 is always a factor — 1 divides every number
Including the number itself — don't forget to list n as a factor of n
Entering zero or negative numbers — only positive integers work
Confusing factors with multiples — factors divide the number; multiples are divisible by it
Tips
Prime numbers (2, 3, 5, 7, 11, etc.) have exactly 2 factors: 1 and themselves
Perfect squares (1, 4, 9, 16, 25, etc.) always have an odd number of factors
The more factors a number has, the more composite (non-prime) it is
Prime factorization is unique—every integer above 1 has one and only one prime factorization
Frequently asked questions
What's the difference between factors and multiples?
A factor divides into a number evenly. A multiple is produced by multiplying a number. For 12: factors are 1, 2, 3, 4, 6, 12; multiples are 12, 24, 36, 48, etc.
Why is 1 a factor of every number?
Because any number divided by 1 equals itself with no remainder. By definition, 1 is a factor of all integers.
What is prime factorization used for?
Prime factorization is fundamental in cryptography, simplifying fractions, finding GCD and LCM, and understanding number structure in mathematics.
Can I find factors of large numbers?
Yes, the calculator works for any positive integer within browser precision (up to about 15 significant digits).
What makes a number prime?
A prime number has exactly two distinct factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. (1 is not prime.)
How is prime factorization notation written?
Use exponential form: 2² means 2 × 2, 3³ means 3 × 3 × 3. For 60 = 2² × 3 × 5, the exponent 1 is usually omitted.