One and two.
The number 1 is prime, but not even.
It will be Odd if the original number was Odd - you have O + O + O = (O + O) + O = E + O = O Otherwise it will be Even if the original number was Even - you have E + E + E = (E + E) + E = E + E = E ------------------------------ Algebraically: For an odd number x = 2n + 1 where n is an integer 3x = 3 × (2n + 1) = 6n + 3 = 6n + 2 + 1 = 2(3n + 1) + 1 = 2m + 1 where m = 3n + 1 which is an odd number For an even number x = 2n where n is an integer 3x = 3 × 2n = 6n = 2(3n) = 2m where m = 3n which is an even number
Every palindrome with an even number of digits is divisible by 11. The easiest way to see this is to recall the divisibility rule by 11: if a number X is written as ABCDEFG... (here A,B,C, ... are digits), then it's divisible by 11 if and only if the sum A-B+C-D+E-F+G-... is divisible by 11. In a palindrome with an even number of digits, each digit will appear in an odd position and in an even position, so when we calculate this sum, it will be added once and subtracted once, canceling. Since all the digits cancel, the sum A-B+C-D+... will be 0, which is divisible by 11. So the original number ABCD....DCBA was also divisible by 11.
Every,even and eating
By looking at its factor patterns.
14
If it's just factors, then any number have an even amount of factors. Let a be any number, a = 1 a so a have two factors, 1 and a. Two is even. But if the question is what number have an even amount of PRIME factors, then it is different. Because if a is not prime, the might exist another two numbers b and c != 1 such that a = b c. and also, b is not prime, b = d e So a = bc = de c = c d e So a have three prime factors (1 is not prime for some reason) Then this question is less trivial: 6 have only prime factor 2 and 3, 10 only have prime factor 2 and 5, they are even. but 9 only have prime factor 3, so it's not an even amount, so 9 is not.
19
16 and The eighth even number
yes, only numbers like pi and e are irrational numbers
No. Two odd numbers added together always give an even number. Two even numbers added together always give an even number. An odd and an even number added together always give an odd number. So, if we have 5 odd numbers - a, b, c, d and e a + b will be even c + d will be even So if (a + b) + (c + d) is even, adding e to that will have to be an odd number - but 50 is even, so it cannot be done.
No. "Pi", "e", and the square root of 2 are all real and irrational.