Prime Factors

Let's now consider something more interesting. In mathematics we often want to know whether a number like 63 is divisible by anything other 1 and 63. We know that in this case 63 is divisible by 3, 7, 9, and 21. But what about a number like 61? Well, no whole number will divide into 61 other than 1 and 61, so 61 is what is known as a prime number.

So consider the number 63 again. Using our known factors of 3, 7, 9 and 21 we find that 63=3x21 or 63=7x9 (there is no other combination of two factors). But 9=3x3 and 21=3x7, so in fact 63=3x3x7. This last representation is irreducible, as 3 and 7 are prime numbers themselves and so 3x3x7 represents the prime factors of 63. In fact, composite numbers like 63 are all constructed from a unique set of prime factors.