Author:
Louise Ward
Date Of Creation:
4 February 2021
Update Date:
24 June 2024
Content
If you know how, finding the factors in a number is as simple as counting 1 2 3. But with larger numbers, you can't just count each factor. This is a good trick to be able to find the factors that are in an integer.
Steps
Choose a number. It can be any number, but it's best to start with simpler numbers.
- For example, choose 72. However, it can also be considered a variable.
Find the prime factor of the selected number. There are many ways to do that, but normally, creating a factor tree is simple. According to number theory, this is an efficient method because every integer (except -1, 0 and 1) has a certain number of prime factors and when multiplied, the product is exactly the same number. Remember that 0 and 1 are not must be prime.- 72 is broken down into 2 and 36; 2, 6 and 6; and finally: 2, 2, 3, 2, 3, which equates to 2 * 3.
Take all exponents and add one to each number.- In the examples 2 and 3, the exponents are 3 and 2 - adding one to each gives us 4 and 3.
Get the total number of adjusted exponents..
- 4 x 3 = 12. 72 has 12 factors - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Method 1 of 1: Example
7540
- Decomposition to prime factors - 25 (29) (13), because x = x, 29, 13, and 5 all have exponents of 1.
- Add 1 to the exponent. 3, 2, 2, 2.
- Get the total number of adjusted exponents. The 7540 has 24 factors.
15802
- Decomposition to prime factors - 2 (7901).
- Adjust exponent - 2, 2.
- Plus. The number 15802 has four factors - 1, 2, 7901, 15802. 7901 is a prime number.
Advice
- The reason for adding one to each exponent is because of the power of the number zero. That is, by 2, it is possible to decompose into four power combinations: 2, 2, 2 and 2. You can multiply 2 by 72 and still get 72 because x = 1 (where 0 is a special exception - it's an unspecified case)
- This article tells you how many factors there are in a number, without showing how to Analyze Some Numbers into Factors.
