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I don't understand how to work out what a prime number is
A prime number is a positive whole number (natural number) which cannot be divided into smaller whole numbers. In short, it can only be divided (integer division) by itself and 1.
First prime number is 2, then 3, 5, 7, 11, 13, 17, 19,
To generate a list of prime numbers the Greek Eratoshenes used a method called now the sieve Eratosthenes.
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2) Cross off number 1, because all primes are greater than 1.
3) Number 2 is a prime, so we can keep it, but we need to cross off the multiples of 2 (i.e. even numbers).
4) Number 3 is also a prime, so again we keep it and cross off the multiples of 3.
5) The next number left is 5 (because four has been crossed off), so we keep it and cross of the multiples of this number.
6) The final number left in the first row is number 7, so cross off its multiples.
7) You have finished. All of the "surviving" numbers (coloured in white below) on your grid are prime numbers.
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"Prime Factorization" is finding which prime numbers multiply together to make the original number.
Example : What are the prime factors of 12 ? It is best to start working from the smallest prime number, which is 2, so let's check:
12 ÷ 2 = 6
Yes, it divided evenly by 2. We have taken the first step!
But 6 is not a prime number, so we need to go further. Let's try 2 again:
6 ÷ 2 = 3
Yes, that worked also. And 3 is a prime number, so we have the answer:
12 = 2 × 2 × 3
As you can see, every factor is a prime number, so the answer must be right.
Note: 12 = 2 × 2 × 3 can also be written using exponents as 12 = 22 × 3
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