In mathematics, a factor is a divisor of a given integer that divides it fully without leaving any remainder. A factor is a number that entirely divides another number with no remainder. We encounter factors and multiples on a regular basis. They are used to arrange goods in a box, handle money, detect patterns in numbers, solve ratios, and work with expanding or reducing fractions, among other things.
Factorization or factoring in mathematics is the process of representing a number as a product of several factors. For example, 4 × 8 is a factorization of the integer 32, and (4,8) are factors of 32.
Let’s learn about factorization in detail by using the numbers 24 and 32 as examples.
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.
How to Find the Factors of 24?
A number is factorized when it is written as a product of its factors. The multiplication method is the most often used method for determining the factors of a number. Let’s find the factors of 24 using the multiplication method.
Factors of 24 using Multiplication Method
Let us find the factors of 24 using the multiplication method using the following steps.
- 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, and 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. We acquire all of the factors this way.
- After noting the list, we receive all the factors of 24 starting from 1 up there, descending down, and then going back up to 24. This provides us a complete list of all the 24 factors.
As a result, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 32
The factors of 32 are the integers that may be split equally into 32. There are six 32-number factors: 1, 2, 4, 8, 16, and 32. All 32 factors add up to 63. It has Factors 1, 2, 4, 8, 16, 32, as well as Pair Factors (1, 32), (2, 16), and (3, 32). (4, 8).
What are the Factors of 32?
- A number’s factor is a number that divides it fully without leaving any residual.
- The composite number 32 is an even number. If a number has more than two elements, it is said to be composite.
- Consider the number 23. It simply contains two factors, 1 and 23. It is prime because it is only divisible by 1 and 23. Consider the number 48. It has more than two factors, hence it is composite.
The integers that divide 32 without leaving a remainder are known as factors of 32, and they are 1, 2, 4, 8, 16, and 32.
How to Calculate Factors of 32?
- Let’s start with the whole number 1 and work our way up to the factors of 32.
32 ÷ 1= 32
- Next, divide 32 by 2.
32 ÷ 2= 16
- Then we get.
32 ÷ 4= 8
- Similarly, we finish up calculating all of the factors of 32.
1, 2, 4, 8, 16, and 32 are all factors of 32.