Prime Factors

A prime factor is a factor of a prime number that is the given number. Factors are numbers multiplied together to get another number. On the other hand, a prime number is a number with two factors, that is; 1 and the number itself. For instance, let’s take the number 30. We know that 30=5×6, but 6 is not a prime number. The number 6 can be factorized further as 2×3, which are prime numbers.

Let’s learn more about prime factorization using solved examples and practice questions.

Prime factorization

There are many ways to find a number’s prime factor. However, the common method is by a prime factor tree. A factor tree is a basic ingredient of a prime factor. The other method is division. Here are examples.

Factor tree method

Follow these steps:

●        Use the given number as the root of the tree.

●        Write the pair of factors as the factor tree branches.

●        Factorize composite numbers and put down the factor pairs as branches.

●        Repeat the above step until you get the prime factors of the composite factors.

Example: Find the prime factors of 19910 using the factor tree method

Division method

●        First, divide the give by a number using the smallest prime number.  Note that it should divide the given number exactly.

●        Again, use the smallest prime number to divide the quotient.

●        Repeat the steps until the quotient is 1.

●        Lastly, multiply all prime factors.

Example: Find the prime factors of 40 using the Division Method

Prime number chart

Some of the prime numbers are 2, 3, 5, 7, 11,13,17,19, 23, 29, 31, 3, 41, 47 and 53.  These numbers cannot be factored to smaller numbers. You can find a list of other prime numbers here on our prime number chart 0 -1000

23     5       7       11     13     17     19     23     29     31     37     41   43  47   53     59     61    67     71      73    79     83     89     97     101   103   107  109     113   127  131   137   139   149    151   157  163   167   173   179 181    191 193   197   199   211   223   227   229   233   239   241   251   257   263    269  271   277  281   283   293   307   311   313   317   331   337   347    349   353   359   367   373 379   383   389    397    401  409   419  421  431  433   439   443   449  457   461   463   467   479   487 491   499     503   509     521   523   541  547   557   563   569   571   577   587   593   599   601   607   613   617   619   631   641   643   647   653  659    661    673   677   683   691   701   709   719   727   733   739   743 751   757     761   769   773   787   797   809   811   821   823   827   829   839  853  857 859   863   877   881   883   887   907   911   919  929  937  941   947 953  967   971   977  983    991   997

Prime factorization applications

The main applications of the prime factorization are:

Cryptography:  This is a method where information is communicated through codes to protect it. Prime factorization allows coders to create unique codes with numbers that can easily be stored or processed on computers.

LCM and HCF using fundamental theorem arithmetic: you use fundamental theorem arithmetic to find LCM and HCF of two numbers. First, you need to find the factorization of these numbers. Here are the things to keep in mind:

●        LCM: is the product of the “greatest power” of every common prime factor.

●        HCF: is the product of the “smallest power” of every common prime factor