# How many composite numbers are between 1 and 50?

Apr 5, 2016

Total $33$ composite numbers.

#### Explanation:

Between $1$ and $50$, we have following numbers as composite.

{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49}

Total $33$ composite numbers.

May 26, 2017

$48 - 15 = 33$ composite numbers between $1 \mathmr{and} 50$

#### Explanation:

Composite numbers are those which have $3$ or more factors:

Prime numbers are those which have exactly $2$ factors:

There are more composite numbers than prime numbers, (can you explain why this is so?)

So it will be easier to count the prime numbers and subtract them.

There are $50$ numbers FROM $1$ to $50$

Therefore there are $48$ numbers BETWEEN $1 \mathmr{and} 50$. which are excluded.

There are $15$ prime numbers less than $50$, which are:

$2 , \textcolor{w h i t e}{.} 3 , \textcolor{w h i t e}{.} 5 , \textcolor{w h i t e}{.} 7 , \textcolor{w h i t e}{.} 11 , \textcolor{w h i t e}{.} 13 , \textcolor{w h i t e}{.} 17 , \textcolor{w h i t e}{.} 19 , \textcolor{w h i t e}{.} 23 , \textcolor{w h i t e}{.} 29 , \textcolor{w h i t e}{.} 31 , \textcolor{w h i t e}{.} 37 , \textcolor{w h i t e}{.} 41 , \textcolor{w h i t e}{.} 43 , \textcolor{w h i t e}{.} 47$

Therefore there are
$48 - 15 = 33$ composite numbers between $1 \mathmr{and} 50$.