Question

How many composite numbers are between 1 and 50?

Answer 1

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.

Answer 2

`48-15 = 33` composite numbers between `1 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 and 50`. which are excluded.

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

`2,color(white)(.)3,color(white)(.)5,color(white)(.)7,color(white)(.)11,color(white)(.)13,color(white)(.)17,color(white)(.)19,color(white)(.)23,color(white)(.)29,color(white)(.)31,color(white)(.)37,color(white)(.)41,color(white)(.)43,color(white)(.)47`

Therefore there are
`48-15 = 33` composite numbers between `1 and 50`.