All divisors of an integer
Calculator for calculating all divisors of an integer
This function calculates the set of divisors of an integer and the number of divisors. The divisor set of a number is the set of all numbers by which this number is divisible without a remainder.
To perform the calculation, enter the integer whose divisors are to be calculated, then click on the 'Calculate' button.
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Description of the divisor of a number
The divisors of a number are all numbers by which this number can be divided without a remainder. Every number can be divided at least by itself and 1. A number that is greater than 1 and can only be divided by itself and by 1 without a remainder is called a prime number. Any other number that can be divided by more than two numbers is called a composite number.
The divisor of a number is the number of numbers by which a number is divisible without a remainder. Every natural number has at least two divisors, itself and one.
Calculate all divisors of a number
There is a systematic method for calculating all divisors of a number.
Factorize a number
Break the number down into its prime factors. This means writing the number as a product of prime numbers.
Example
Find all divisors of the number 24.
Factor 24 into prime factors:
\[24=2×2×2×3=2^3×3^1\]
Determine divisors
Use prime factorization to find all divisors. The formula for the number of divisors is:
\[\text{ number of divisors}=(e_1+1)×(e_2+1)×⋯×(e_n+1) \]
where \(e_1,e_2,…,e_n \) are the exponents of the prime factors.
For 24 the \[\text{ number of divisors}=(3+1)×(1+1)=4×2=8\] So there are 8 divisors.
Write down the divisors
The divisors result from all possible combinations of the prime factors:
\[ 1,2,3,4,6,8,12,24\]
General method:
- Start with the number 1 (1 is always a divisor).
- Check every number from 2 to half of the given number to see if it is a divisor.
- The number itself is always a divisor.
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