Factors of a number are the numbers which can be multiplied to get another number. For example, factors of the number 15 is 5 and 3. If we multiply 5 and 3, we will get the number 15. There are a number of methods of finding the factors of a number. The factors of a two digit number is easier to find, while the factors of number with four or more digit is a bit difficult to be identified. However, there are methods that can help in easier identification of the factors, even for the critical numbers.
Factors of a number can be considered as a number which is multiplied together to form and deliver as a product. One of the most significant way of thinking of this is that every number is a product of multiple factors. In order to find the factors of a number, it is necessary to understand the process of breaking up of the numbers into different component factors. Breaking up of a number into component factor is an important mathematical skill that is mainly used not only in the mathematical arithmetic but also in algebra, calculus and beyond.
Factoring a number can be done in a very basic form. In order to begin with the factoring, a number is to be chosen and written down on a paper. For example, a number 12 is chosen, the factoring of the number can be done in the following manner-
12 = 12 x 1
12 = 6 x 2
12= 3 x 4
Factoring in the above manner is possible as two or more number can multiply to deliver the first number. An integer can be described as the product of 1 and the number itself. It is observed that in order to understand the process of development of the factors, it is quite essential to understand and identify the multiplication problems that equals to a particular number. Therefore, in the above example, the number 12 has factors which include 1, 2,3,4,6 and 12. It is observed that even number can be significantly easy to factor as it will definitely have 2 as a factor.
One of the basic steps of factoring is to check that whether after first factoring, a number can be factored again or not. This is generally true for the large number as lots of numbers, mainly the large numbers can generally be factored a number of times. For example, a number 12 can be factored as 2 X 6. It is observed that the digit 6 can be factored once again into 2 x 3. Therefore 12 can be easily factored as 2 x (3x2).
Another rule of formatting is that one needs to stop factoring when a prime number is reached. Prime number can be described as a number that are greater than 1 and are evenly divisible by the number themselves and also with 1. Example of prime number include 2, 5, and 7,11,13,17 and so on. While factoring a number, it is necessary to reduce each factor at least one time with an aim of finding out the correct factor of the number. Taking the same example, the number 12 is reduced to 2 X 6 and 6 is further factored in 2 x 3. If the factors are further factored, we will have factors such as (2 × 1) × ((2 × 1) (3 × 1)), which may not be useful for consideration and therefore can be avoided. The factorization process can be easily done for the two digit numbers. However, for other larger numbers, the factoring process may not be easy as a lot of numbers might needed to be factorised. There is no significant difference between the factoring process of the positive as well as the negative number. The factoring process of a negative number -60 is indicated as follows- The factorization process of -60 is indicated as follows-
-60 = -10 × 6
-60 = (-5 × 2) × 6
-60 = (-5 × 2) × (3 × 2)
-60 = -5 × 2 × 3 × 2.
Therefore, the factorization process is quite easy. However, factorization of large number can be a time consuming matter. However, it is necessary to find out a process or method that can help in effective factoring of the large numbers as well. It is fairly easy to find factors to the small integers while doing the same for the large integers can be a daunting task. It is quite difficult to break a 4-5 digit number into prime factors.
Write down all the factors of the following numbers :(i), 28(ii) 80(iii)144
= 2 x 7 x 2
Therefore, the factors of the number 28 is 2, 7 and 2
= 2 x 2 x 20
= 2 x 2 x 2 x 10
= 2 x 2 x 2 x 2 x 5
Therefore, the factors of 80 are, 2, 2, 2, 2 and 5.
= 2 x 2 x 36
= 2 x 2 x 2 x 18
= 2 x 2 x 2 x 2 x 9
= 2 x 2 x 2 x 2 x 3 x 3
Therefore the factors of the number 144 is 2, 2, 2, 2, 3 and 3.
In the above three questions, the factorisation is done is a most basic process. Since all the numbers were even numbers, the process of factoring the number became easier. Most of the numbers in the above three factorization were divisible by 2 and therefore, calculation of factors of each number became quite easy.
As calculated, the factors of the number 28 is 2, 7 and 2, the factors of 80 are, 2, 2, 2, 2 and 5 and the factors of the number 144 is 2, 2, 2, 2, 3 and 3. The factorization process for all the given three numbers are stopped since a prime numbers are reached in each of the cases.
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