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Prime numbers and prime decomposition
Prime and composite numbers, factor trees, and writing a number as a product of its prime factors using index notation.
Prime and composite
A prime number has exactly two factors: $1$ and itself. The primes start $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, \ldots$ A composite number has more than two factors. The number $1$ is neither.
Prime decomposition
Every composite number can be written as a product of primes in exactly one way. Build a factor tree: split the number into any two factors, and keep splitting until every branch ends in a prime.
Write $360$ as a product of prime factors in index form.
Which is prime?
$29$ has only factors $1$ and $29$.
Which is composite?
$51 = 3 \times 17$.
$360$ as a product of primes is:
$8 \times 9 \times 5 = 360$.
$60$ as a product of primes is:
All factors must be prime.
How many primes are less than $10$?
$2, 3, 5, 7$.
What is the only even prime?
All other even numbers have $2$ as a factor.
What is the largest prime factor of $100$?
$100 = 2^2 \times 5^2$.
How many different prime factors does $90$ have?
$90 = 2 \times 3^2 \times 5$.
New numbers every time. Keep going until you get five in a row.