Hi P&A

Assuming you are looking to write a number as a product of its primes.

A prime number has two distinct factors, itself and 1.

2 is the only even prime number, becasue it only has two factors, 2 and 1.

Any number can be written as a product of its primes.

First identify the prime numbers using eratosthenes sieve.

http://www.teachingideas.co.uk/maths/prime.htm
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71

are the first twenty prime numbers.

Now choose at random any number, say 48

Start by dividing by 2

48 divided by 2 equal 24

24 divided by 2 equals 12

12 divided by 2 equals 6

6 divided by 2 equals 3

3 is a prime number so you cannot continue

48 can be written as 2 x 2 x 2 x 2 x 3, the product of its primes.

Try again with 63

63 is an odd number so cannot be divided by 2, so try 3

63 divided by 3 is 21

21 divided by 3 is 7

7 is a prime number so you cannot continue

63 can be written as 3 x 3 x 7, the product of its primes

Try again with 35

Can´t divide by 2, Can´t divide by 3, try 5

35 divided by 5 equals 7

7 is a prime number so you cannot continue

35 can be written as 5 x 7

Try 71

Can´t divide by any prime number except itself.

So 71, must be a prime number.

Keep practicing.

The product of primes is used to identify highest common factors and lowest common multiples of different numbers.

Hope this helps

Regards

Mike