A prime number is a number that can only be divided by itself and 1 without any other value being left over.
Prime numbers have been known about since ancient times as they form an important part of the way we create our security codes today. The first time a “prime” number was discovered it was thought to be significant as it was connected with our physical world as opposed to anything else that might exist. This means that one cannot predict what a prime number will look like based on its previous factors – i.e., one cannot predict its square root, or how many digits it has, etc.
The first few prime numbers are: 2, 3, 5, 7 9 11 13 17 19 23 etc…
So what’s a factorization? prime factorization for short, means breaking a number down into its smaller “factors”, also known as divisors. For example: 12 = 2 x 2 x 3 which can be rewritten as 12 = 2 x 2 x 3 = 23.
In other words, we broke down 12 into factors (2x2x3) and then rearranged these factors into a new product (23). One can do this with any whole number, i.e., work out the prime factors of a number and then put them together as a new product.
A multiple is a factor with more than two numbers, whereas a factor has only one or two numbers being multiplied together.
An example of this would be 12 = 2 x 2 x 3 which is an example of three different multiples as there are three numbers in total being multiplied together to give us 12. Or we could say 12 = 4×3 as there are only two numbers (4 and 3) multiplied together to give us 12.
Factors and multiples are also closely related to the idea of primes as every number has a finite amount of factors and multiples. For example: 30 is an odd number, as it cannot be expressed as 2 x 15 (exactly). It can, however be expressed as 5 x 6 or 3 x 10 , etc.
In general terms, one should have noticed that 1 is not a prime number – this might seem obvious, but sometimes people will talk about ‘the’ prime number rather than ‘a’ prime number. We know 1 isn’t a prime because it divides by itself – i.e. 1 x 1 = 1. It can also be expressed as 12, or 123 or any other combination that means the same thing!
However, some special types of numbers are called ‘prime numbers’ but aren’t actually prime when you find out their real factorization…
An example of this is 6. 6 is a composite number – not a prime number – because it can be written in more than one way. We call these types of numbers composites rather than primes because it turns out they’re actually made up of lots of smaller numbers working together to give one big result, whereas primes can only be divided by themselves and 1.
The number 2 is the smallest prime number, and it is also the only even prime number. Every other prime number is odd, which means that when one is multiplying two integers together to get another integer, when at least one of them (and usually both) are divisible by 2, then when you divide that product by 2 you will end up with a remainder of 0 . In other words, if one multiplies 3 and 5 for 15 and then divides it by 2 , the remainder will be 0 because both numbers were divisible by two from being factors of 2.
In factoring integers using prime factorization, all quantities except for one will be prime factors.
For example: 25 = 5*5 or 52 = 7*7
This would be if the largest divisible number was the same as the smallest prime factor, which is known as a square number because its multiples are squared. For example, 49 is divisible by 7 because both 49 and 49*49 have a remainder of 0 when divided by 7 . By this logic, all numbers that fit into the category of being a perfect square would have a prime factorization of n*n where n is an integer.
For example: 25 = 5*5 or 52 = 7*7
Some examples of perfect squares: 16 , 36 , 100 , 216
There are the greatest common factor available alongside LCM and GCF. One can know more about prime numbers and common factors; they have to access Cuemath website.