In mathematics, introduction to numbers is often shown as a number line; usually, whole numbers written with each number symbol separated at a uniform distance. Each number to the right is one step more than the number before it and one step less than the number ahead of it. This is one of the elementary observations when one looks at a number line, another pattern one can look into number line is what is called factors and to get the prime factors of a number is called prime factorization.
To learn maths, one can tread many different ways in a number line, for example, the most straightforward would be to tread one step at a time hence giving us one relationship among these numbers. Another way can be to hop on alternate numbers so one would come across 2, 4, 6, 8, etc. which is then represented as 2x in algebra as an expression. Another arithmetical tool called prime factorization is perhaps more hidden when one is just looking at the number line. Let us see what prime factorization is.
Consider a number ( any number), let us take the number 10, for example. Now try and think about what different ways one can get the number 10. For example, 9 + 1 would be 10 and so would be 11 – 1 or 8 + 2, etc. the combinations are too many. If we say, write down the different ways one can get 10 due to the multiplication of two whole numbers. So, now let us see how many different ways we can get this. We know anything multiplied by 1 remains unchanged so one way would be 10 × 1 = 10.
Another one, by coincidence we are reminded that 2 * 5 is also equal to ten and the reason for this intelligent coincidence is because we noticed the five fingers we have in each of our hands.
That’s it we cannot think of any more ways. So let’s see the answers we have got:
- 10 = 10 × 1
- 10 = 5 × 2
Even if you don’t understand it yet don’t bother just remember at this point that 1, 10, 5, 2 are prime factors of number 10.
Definition of Prime factors would be when we write a natural number as a product of two or more whole numbers then those are called the factors of that particular number, or in other words, it can be said that the natural number is expressed in factored form. There is also prime factorization where a number is written as a product of its prime factors. A prime number is a number that has only two factors.
Like the factors of 6 are 3 and 2, as when 3 and 2 are multiplied together, the product is 6.
Also, let’s see the factors of 15, they would be 3 and 5 as 3 x 5 = 15; hence 3 and 5 are called factors of 15, and the number 15 is called the product.
Remember a prime is a number that is only divisible by itself or the number 1.
How to find out prime factors, if the number is small one can perhaps just do it orally for example 21 one easily knows it would 3 and 7. But how do we get prime factors for a bigger number?
The way to find the prime factor of a big number is to approach the number bit by bit starting with the lowest prime number which is 2, check if the number can be divided leaving zero remainder. Continue dividing by 2 till the time you can and if it is not divisible by 2 anymore then pick the next smallest prime number which is three and divide the number and repeat till the number is completely divided. Thus we will get the numbers that had made that number.
For example, the number 100, Divide by 2, quotient 50, Divide by 2, quotient 25, Divide by 5 as the next largest prime number is not divisible by 3, quotient 5, Divide by 5, quotient 1. So the prime factors are 2 and 5. Factors are 2 × 2 × 5 × 5.
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