# Prime Factorization

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Prime Factorization

Prime factorization in simple terms, refers to the process of multiplying the available prime numbers in order to get a given number. To understand the concept of prime factorization better, it is important to understand which numbers are termed as the prime numbers, as well as the meaning of the word factorization. Prime numbers can be described as those integers that can only be multiplied by number one (1) or the number itself. Examples of prime numbers include numbers 2, 3,5,7,11,13 and 17.

On the other hand, factors refer to numbers that can be multiplied collectively to give a certain number. The process of putting the multiples of a given number starting from the least to the greatest numbers is referred to as factorization. Examples of factors include numbers 2 and 3 which are multiples of 6, since 2 × 3 = 6. Factors of prime numbers such as 2 and 3 in the above multiplication problem are known as the prime factors.

A teacher can use two methods to teach kids on how to get the prime factorization of given numbers. In the first method, one needs to identify the prime integers that are divisible by that number and this can be done by finding out whether the number can be divided by all the known prime numbers starting with the least prime number, which is 2.

This division process should be repeated for every prime number getting up as further as one can go to attain the prime multiples of the given number. It is important to note that the factors of any numbers should only be arranged starting from the smallest prime number upwards. For instance, to get the prime factorization of number 50, the first step should be checking whether it is divisible by prime number 2 as follows

50 × 2 =25

Since 50 is divisible by 2, then 2 is a factor of 50. But because 25 is not a prime number, one needs to further factorize it with other prime numbers again starting with the least number. In this case digit 25 is not divisible by 2 and 3 but it is divisible by 5 since 5×5 =25. This is the furthest one can get and thus the prime factorization of number 50 is

2×5 ×5.

This can also be written with exponents whenever there are similar numbers, in this case 5×5 can be replaced with an exponent to be 2 × 52. .

In the second method, other than starting with the smallest divisible prime number when looking for prime factorization, one can break the given numbers into two greatest multiples and factorize them downward further. For instance to work out the prime factorization of 80, its greatest multiples are 8 × 10 = 80. The prime factors of 8 are

2 × 2 × 2= 8

And the prime factors of 10 are

2 × 5= 10.

The prime factors of 80 are therefore the combined factors which are 2× 2 × 2 × 2×5 = 80 and can be written as exponents like follows

24 ×5 =80. This would perhaps be the best approach to teaching kids, as breaking it down to the two simple multiples and then factorizing each individually is a bit easier.