24
16, which is the square of 4, is a two digit even number.
97 has two factors.
63? But it has more than two one-digit factors.
The largest two-digit even number is 98. In the decimal system, each digit can range from 0 to 9, but for a two-digit number, the first digit cannot be zero. Since we are looking for an even number, the last digit must be an even number, which leaves us with 0, 2, 4, 6, or 8. Among these options, 8 is the largest even digit, resulting in 98 as the largest two-digit even number.
63
The first 2 digit integer is 10. This is an even number and is therefore the answer.
A two-digit number with exactly 7 factors must be of the form ( p^6 ), where ( p ) is a prime number, because the number of factors of ( n = p^e ) is ( e + 1 ). The only prime number that, when raised to the sixth power, results in a two-digit number is 2, since ( 2^6 = 64 ). Therefore, 64 is the only two-digit number that has exactly 7 factors.
24
36
25
63.
The two-digit factors of 100 and 1000 are all composite.