Question

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

Answer 1

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.

Answer 2

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.