Is 23,27, and 29 a prime number? Show ur work

Take 23 and divide by 2.

23/2=11.5

That means all the numbers 12 and above would be repeating numbers.

Example:

4*8 is the same as 8*4

So that's means we have the numbers 2-12:

2,3,4,5,6,7,8,9,10,11,12

So because 23 isn't an even number, we know that no even number is a factor of 23.

So now we have the numbers

3,5,7,9,11.

Now the rule for 3 is adding the digits and if the sum is a multiple of three, than it is a factor of three.

2+3=5

Since five isn't divisible by three, we know that 3 is not a factor of 23. Because we know three is not a factor, we also know 9 is not a factor.

Now we have the numbers

5,7,11

The rule for 5 is as follows: if the number ends in a 0 or a 5, then 5 is a factor or the number.

Since 23 does not end in 0 nor 5, we know five is not a factor.

Now we have the numbers

7,11

To find 7 and 11, we are going to divide 23 by each. If it comes out evenly, then it is a factor.

23/7=3 + (2/7)

23/11=2 + (1/11)

Since neither came out clean, we know that neither are factors. From the information above, we can conclude 23 is a prime number.

Take 27 and divide by 2.

27/2=13.5

That means all the numbers 14 and above would be repeating numbers.

Example:

4*8 is the same as 8*4

So that's means we have the numbers 2-14:

2,3,4,5,6,7,8,9,10,11,12,13,14

So because 27 isn't an even number, we know that no even number is a factor of 27.

So now we have the numbers

3,5,7,9,11,13

Now the rule for 3 is adding the digits and if the sum is a multiple of three, than it is a factor of three.

2+7=9

Since 9 is divisible by three, we know that 27 is not a prime number

Take 29 and divide by 2.

29/2=14.5

That means all the numbers 15 and above would be repeating numbers.

Example:

4*8 is the same as 8*4

So that's means we have the numbers 2-15:

2,3,4,5,6,7,8,9,10,11,12,13,14,15

So because 29 isn't an even number, we know that no even number is a factor of 29.

So now we have the numbers

3,5,7,9,11,13,15

Now the rule for 3 is adding the digits and if the sum is a multiple of three, than it is a factor of three.

2+9=11

Since 11 isn't divisible by three, we know that 3 is not a factor of 29. Because we know three is not a factor, we also know 9 and 15 are not factors

Now we have the numbers

5,7,11,13

The rule for 5 is as follows: if the number ends in a 0 or a 5, then 5 is a factor or the number.

Since 29 does not end in 0 nor 5, we know five is not a factor.

Now we have the numbers

7,11,13

To find 7, 11, 13, we are going to divide 29 by each. If it comes out evenly, then it is a factor.

29/7=4 + (1/7)

29/11=2 + (7/11)

29/13=2 + (3/13)

Since none of them came out clean, we know that none of them are factors. From the information above, we can conclude 29 is a prime number.

23 is a prime number because it is only divisible by (has factors of) 1 and itself (23).

27 is NOT a prime number because it is divisible by more than 1 and itself (also 3 and 9).

29 is a prime number because it is only divisible by 1 and 29.