What are all the composite numbers between 31 and 51?

2 Answers
Nov 1, 2017

See a solution process below:

Explanation:

A composite number is: a whole number that can be divided evenly by numbers other than 1 or itself.

Because every even number is divisible by #2# all of the even numbers between 31 and 53 are part of the solution set for this problem:

#32, 34, 36, 38, 40, 42, 44, 46, 48. 50, 52#

Every number ending with #5# is evenly divisible by #5# so we can add these numbers to the solution set:

#32, 34, color(red)(35), 36, 38, 40, 42, 44, color(red)(45), 46, 48. 50, 52#

This leaves:

#33, 37, 39, 41, 43, 47, 49, 51#

The digits in #33#, #39# and #51# are evenly divisible by #3# so we can add them to the solution set:

#32, color(blue)(33), 34, color(red)(35), 36, 38, color(blue)(39), 40, 42, 44, color(red)(45), 46, 48. 50, color(blue)(51), 52#

This leaves:

#37, 41, 43, 47, 49#

#49# is #7^2# so this can be added to the solution set:

#32, color(blue)(33), 34, color(red)(35), 36, 38, color(blue)(39), 40, 42, 44, color(red)(45), 46, 48. color(orange)(49), 50, color(blue)(51), 52#

This leaves: #37, 41, 43, 47# These are all prime numbers and therefore not composite numbers so the solution is:

#32, color(blue)(33), 34, color(red)(35), 36, 38, color(blue)(39), 40, 42, 44, color(red)(45), 46, 48. color(orange)(49), 50, color(blue)(51), 52#

Nov 4, 2017

#32," "33," "34," "35," "36," "38," "39," "40," "42," "44," "45," "46," "48," "49," "50#

Explanation:

All natural numbers except #1# are either prime or composite,

There are fewer prime numbers than composite numbers.

So, in order to find all the composite numbers between #31 and 53#, it is easier to just remove all the prime numbers.

The prime numbers between #31 and 53# are:

#37," "41," "43," "47#

Removing these leaves us with:

#32," "33," "34," "35," "36," "cancel37," "38," "39," "40," "cancel41," "42," "cancel43," "44," "45," "46," "cancel47," "48," "49," "50#