Factor Calculator – Find All Divisors
Enter a number and this factor calculator lists all of its factors. It also shows how many there are, their sum, the factor pairs, the prime factorization and whether the number is prime or perfect. With a second number you get the common factors together with the GCF and LCM.
Example: Number 36 → Result: 36 has 9 factors. Source: Wikipedia – Divisor (Teiler, Teileranzahlfunktion). Updated: .
How it is calculated
A factor (or divisor) of a number is a whole number that divides it without a remainder. The number 36 has nine factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36. Every factor has a partner that multiplies with it to give the number again (4 × 9 = 36); the tool shows these pairs as a table.
How the factors are found
- First the number is broken into prime factors; for 36 that is 2² × 3².
- All combinations of the powers produce the factors. The count comes from adding 1 to each exponent and multiplying: (2 + 1) · (2 + 1) = 9.
- The count is odd exactly for perfect squares, because then one pair consists of two equal numbers (6 × 6 = 36).
Types of number and common factors
Primes have exactly two factors. Perfect numbers such as 6, 28 or 496 equal the sum of their proper factors (6 = 1 + 2 + 3). If that sum is larger than the number it is called abundant, if smaller, deficient. With a second number the tool gives the common factors: these are exactly the factors of the greatest common factor (GCF). The least common multiple (LCM) follows from the GCF. For a full breakdown with working use the prime factorization calculator, to reduce fractions the fraction calculator, and for the GCF and LCM of several numbers the GCF and LCM calculator. The tool works up to 1,000,000,000,000.
Frequently asked questions
How do I find all the factors of a number?
Try every number from 1 up to the square root: if d divides without a remainder, then d and its partner n ÷ d are both factors. For 36 these are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6.
What is the difference between a factor and a multiple?
A factor divides into the number (4 is a factor of 36), a multiple is made by multiplying (36 is a multiple of 4). Factors are at most as large as the number, multiples at least as large.
How many factors does a number have?
It depends on the prime factorization: add 1 to every exponent and multiply. 360 = 2³ · 3² · 5 has (3 + 1) · (2 + 1) · (1 + 1) = 24 factors.
What are common factors of two numbers?
Numbers that divide both. They are exactly the factors of the GCF: 48 and 36 have the GCF 12, so the common factors are 1, 2, 3, 4, 6 and 12.
What is a perfect number?
A number equal to the sum of its proper factors. 6 (1 + 2 + 3) and 28 (1 + 2 + 4 + 7 + 14) are the first examples; the next is 496.
Sources and legal basis
- Wikipedia – Divisor (Teiler, Teileranzahlfunktion)
- Wikipedia – Perfect number (perfect numbers, abundant and deficient numbers)
- Wikipedia – Greatest common divisor (ggT, gemeinsame Teiler, kgV)
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