In mathematics, a factor of a number is a number that divides evenly into that number. For example, 2 and 4 are factors of 8 because 8 / 2 = 4 and 8 / 4 = 2. The factors of a number can be found using a variety of methods, including the following:

The Division Method: The division method is the most straightforward way to find the factors of a number. To use the division method, simply divide the number by each of the natural numbers from 1 to the number itself. Any number that divides evenly into the original number is a factor. For example, to find the factors of 8, we would divide 8 by each of the natural numbers from 1 to 8. The results of these divisions are as follows:

8 / 1 = 8

8 / 2 = 4

8 / 3 = 2 2/3

8 / 4 = 2

8 / 5 = 1 3/5

8 / 6 = 1 2/3

8 / 7 = 1 1/7

8 / 8 = 1

The numbers 1, 2, 4, and 8 are all factors of 8.

The Factor Tree Method: The factor tree method is a visual way to find the factors of a number. To use the factor tree method, first draw a tree with the original number at the top. Then, divide the original number by its largest prime factor. This will give you two new numbers. Draw these numbers as branches of the tree, and repeat the process with each new number. Continue this process until you have reached numbers that are prime. The prime numbers at the bottom of the tree are the factors of the original number. For example, to find the factors of 12, we would draw a factor tree as follows:

12

/ \

6 2

/ \ /

3 2 1

The prime factors of 12 are 2 and 3. Therefore, the factors of 12 are 1, 2, 3, 4, 6, and 12.

#### Example: Display Factors of a Number

#### When you run the program, the output will be:

Factors of 40 are : 1 2 4 5 8 10 20 40

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