Study about Factorisation of Numbers like 21 and 24 in Depth

Study about Factorisation of Numbers like 21 and 24 in Depth

A factor in mathematics is an integer that divides the given number precisely. A factor is also referred to as the perfect divisor of a particular number. A factor divides the provided integer by itself, leaving no remainder behind.

Either the multiplication method or the division approach can be used to get the factor of any given number. Factors help us in dividing numbers, arranging objects in rows and columns, and other important daily tasks.

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

Let’s learn about factorization in more depth by taking two numbers i.e., 21 and 24 and finding their factors.

Factors of 21

Factors of 21 are all the whole positive, negative, and whole numbers that divide 21 exactly.

Finding the Factors of 21

Given that all of the numbers by which we can divide 21 perfectly are its factors, we can simply divide 21 by all of the numbers up to 21 to see which ones leave no remainder. If we do this, we will observe that these calculations resulted in an even quotient, as shown below:

21/21 = 1

21/7 = 3

21/3 = 7

21/1 = 21

Therefore, we can say that 1, 3,7 and 21 are factors of 21.

Prime Factorization of 21

The process of representing a composite number as the product of its prime factors is referred to as "prime factorization." We will use the following process to obtain the prime factorization of 21:

●       Divide 21 by the smallest prime number, which divides 21 exactly, say 3

21 ÷ 3 = 7

●       Quotient (7) is divided by the next prime number which perfectly divides 7 and the quotient is obtained.

●       This process continues until the quotient equals 1.

7 ÷ 7 = 1 

●       We discover that 21 has two prime factors, which are 3 and 7.

Factors of 24

Factors of 24 are all the Integers, both positive and negative whole Numbers which you can exactly divide 24.

Factor Pairs of 24

The Factor pairs of 24 are all the conceivable combinations of two factors that add up to 24 when multiplied together. There are 24 Factor pairs that are both positive and negative. All of the positive Factor pairs of 24 that you should be aware of are listed here.

1 × 24 = 24

2 × 12 = 24

3 × 8 = 24

4 × 6 = 24

Therefore, the positive factor pairs of 24 are (1, 24), (2, 12), (3, 8), and (4, 6).

We can think of negative pair factors of 24 because the product of two negative factors yields a positive original number, such as:

-1 × -24 = 24

-2 × -12 = 24

-3 × -8 = 24

-4 × -6 = 24

Therefore, the negative factor pairs are (-1, -24), (-2, -12), (-3, -8), and (-4, -6).

Prime Factorization of 24

Since 24 is a composite number, you can get its prime factors using the simple division shown below.

●       First, divide 24 by the smallest prime factor, which is 2. As a result, you get 24 ÷ 2 = 12

●       Again, because 12 is a composite number, divide it by 2. As a result, 12 ÷ 2 = 6 is obtained.

●       Further division yields 6 ÷ 2 = 3

●       If you divide 3 by 2, you'll receive a fraction number that can't be a Factor.

●       As a result, you must go to the next Prime Number, which is 3. When you divide the number 3 by itself, you get 3 ÷ 3 = 1.

You have now received 1 at the end and cannot continue using the division method.

As a result, the Prime Factorization of 24 is expressed as 2 × 2 × 2 × 3.