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.
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.
