In mathematics, a factor is a divisor of an integer that divides it exactly without leaving any remainder. A factor is a number that divides another number fully without leaving any remainder.

The process of representing a number as a product of several factors is known as factorization or factoring. 4 × 6 is, for example, a factorization of the integer 24 and (4,6) are factors of 24.

Let’s learn about the factorization of a number properly by taking two numbers 15 and 24 as examples.

### Factors of 15

We will learn how to find factors of 15 by combining factor pairs and prime numbers.

#### Factor Pairs of 15

If we look at the factors of 15 as pairs, we can see that 15 is the result of multiplying two numbers. The only integers that arise from listing all the factors of 15 in this context are 1, 3, 5, and 15 as 1 × 15 = 15 and 3 × 5 = 15. As a result, because 15 is a product of prime numbers, only the four aforementioned values are referred to as factors of 15.

#### Prime Factorisation of 15

The integer 15 has several lesser integers in addition to 1 as its divisor. As a result, 15 is referred to as a composite number. The Prime Factorization method will be used to get the factors of 15 as shown below.

The smallest known prime factor is 2. As a result, we'll divide this value by 15 (15 ÷ 2 = 7.5). Because the result is a decimal on (7.5), 2 is not a prime factor of 15.

Let's go on to the following number, 3 (15 3 = 5). Again, dividing 5 by 3 gets 5 ÷ 3 = 1.67, a fractional result (1.67).

Divide 5 by the next prime integer, which is 5 (5 ÷ 5 = 1). We're not continuing with the number division because we got result 1.

As a result, the numbers 5 and 3 are seen as prime factors of 15, where both 3 and 5 are prime numbers.

### Factors of 24

Factors of 24 are numbers that totally divide 24 without leaving any remainder. There are eight 24 factors, with 24 being the largest and 2 and 3 being its prime factors.

#### Factors of 24 using Multiplication Method

Let us use the multiplication method to discover the factors of 24 using the steps below.

• To get the factors of 24 using the multiplication method, we must first determine which integers multiply to give 24. So, starting with 1, we must divide 24 by natural numbers until we reach 9. We must keep track of the numbers that totally divide 24.

• Its factors are the integers that totally divide 24. We write that number and its corresponding pair in a list, as illustrated in the figure above. As we check and list all of the numbers up to 9, we also receive the other pair factor. For example, beginning with 1, we write 1 24 = 24, 2 12 = 24, and so on. Here, (1, 24) makes the first pair, (2, 12) forms the second pair, and so on. So, if we write 1 as a factor of 24, the other factor is 24; and if we write 2 as a factor of 24, the other factor is 12. Same way, we get all other factors as well.

• After noting the list, we receive all the components of 24 starting from 1 up there, descending down, and then going back up to 24. This provides us with an exhaustive list of all the 24 factors.

As a result, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.