Factor Calculator
Find all factors, factor pairs, prime factorization, and the total number of factors for any positive integer.
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How to use this calculator
- 1
Enter any positive integer up to 10,000,000.
- 2
All factors are listed in ascending order, along with factor pairs.
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The prime factorization is displayed using exponent notation (e.g., 2^3 × 3^2).
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The calculator also tells you how many factors the number has and whether it is prime.
Frequently asked questions
What range of numbers does it accept?
Whole numbers from 1 to 10,000,000. Zero, negative numbers and values with a decimal part return “Enter a positive integer”, and anything above ten million returns “Number too large (max 10,000,000)”. It does not round 12.7 to 12 for you.
Is 1 treated as prime?
No. 1 has exactly one factor, itself, so the Is prime? row says No and the prime factorization shows just 1. A prime must have exactly two factors. The calculator tests that, so 97 shows factors 1 and 97 and the answer Yes.
What are factor pairs?
Two whole numbers that multiply to give your number, listed with the smaller first. For 36 the pairs are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6). The pair (6, 6) appears once, and it is a sign that 36 is a perfect square.
Why does a perfect square have an odd number of factors?
Factors usually come in pairs, but in a square the middle pair is the same number twice. 36 has 9 factors, which is odd, while 360 has 24. If the number of factors shown is odd, your number is a perfect square.
Can I get the number of factors from the prime factorization?
Yes. Add 1 to each exponent and multiply. For 360 = 2³ × 3² × 5 that is 4 × 3 × 2 = 24, matching the Number of factors row. For 36 = 2² × 3² it is 3 × 3 = 9.
What does “Sum of factors” include?
Every factor, including the number itself. For 28 the factors add to 56, which is exactly twice 28; numbers with that property are called perfect numbers. For 360 the sum is 1170. If you need the sum without the number, subtract it.
How does it label a prime in the factorization row?
It simply prints the prime itself, so 97 shows 97. Exponents are written with a caret, as in 2^3 × 3^2 × 5, and a number with a single repeated prime such as 10,000,000 comes out as 2^7 × 5^7.
Does it give common factors or the GCF of two numbers?
No, it analyses one number at a time. To find a greatest common factor, run both numbers and compare the factor lists, picking the largest value that appears in both.
All factors, factor pairs and prime factorization
What you get for one number
Enter a positive integer and the calculator lists every factor in ascending order, groups them into pairs, counts them, adds them, labels the number prime or not, and writes its prime factorization with exponents. Everything comes from one search for divisors, so the outputs agree: the factor count is the product of each exponent plus 1, and the factor pairs end at the square root.
| Number | Factor count | Prime factorization | Sum of factors | Prime? |
|---|---|---|---|---|
| 360 | 24 | 2^3 × 3^2 × 5 | 1170 | No |
| 97 | 2 | 97 | 98 | Yes |
| 36 | 9 | 2^2 × 3^2 | 91 | No |
| 28 | 6 | 2^2 × 7 | 56 | No |
| 7919000 | 32 | 2^3 × 5^3 × 7919 | 18532800 | No |
| 10000000 | 64 | 2^7 × 5^7 | 24902280 | No |
Worked example: 360
The default number, 360, has 24 factors, from 1 up to 360, forming 12 pairs from (1, 360) to (18, 20). Its prime factorization is 2^3 × 3^2 × 5, and the exponent rule confirms the count: 4 × 3 × 2 = 24. The sum of all factors is 1170. A number with this many divisors is why 360 shows up in angle measurement, as it splits evenly many ways.
Worked example: a perfect number
For 28 the factors are 1, 2, 4, 7, 14 and 28, and they add to 56. Because the sum including 28 is twice 28, the number is perfect: its proper divisors, everything except itself, add up to exactly 28. The factor pairs (1, 28), (2, 14) and (4, 7) show no repeated middle value, so 28 is not a square.
Primes and squares
A prime appears with exactly two factors, itself and 1, as with 97, whose factor sum is 98. A perfect square such as 36 has an odd factor count because its square root pairs with itself. The number 1 is the odd one out: one factor, not prime. If the prime factorization line shows only the number you typed, you have confirmed that it is prime.
Limits and practical use
Input is limited to whole numbers up to 10,000,000, and decimals or negatives return an error. Use the factor list to simplify fractions, find a common denominator, or check whether a quantity can be split into equal groups. The tool works on one number at a time, so for a greatest common factor you compare two runs yourself.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →