The number that has 12 divisors is 60. The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Since there are 12 divisors for the number 60, it meets the criteria of having 12 divisors. **

Numbers that have 6 divisors are typically square numbers of prime numbers. This is because the divisors of a number come in pairs, except when the number is a perfect square. In the case of a perfect square, one of the pairs of divisors is the same number, resulting in an odd number of divisors. Therefore, numbers like 4, 9, 25, and 49 have 6 divisors. **

Proper divisors of a positive integer are the positive integers that divide the number evenly, excluding the number itself. In other words, proper divisors are the factors of a number that are less than the number itself. For example, the proper divisors of 12 are 1, 2, 3, 4, and 6, as these are the positive integers that divide 12 without leaving a remainder, excluding 12 itself. **

No, one cannot infer the divisors of a number from the divisors of its digit sum. The divisors of a number and the divisors of its digit sum are not directly related. The digit sum of a number is simply the sum of its individual digits, and the divisors of the digit sum do not necessarily have any correlation with the divisors of the original number. Therefore, one cannot make any reliable inferences about the divisors of a number based solely on the divisors of its digit sum. **

The number 6 has four divisors: 1, 2, 3, and 6. These are the numbers that can divide evenly into 6 without leaving a remainder. **

Numbers that have only 4 divisors are square numbers of prime numbers. This is because the only divisors of a square number are 1, the number itself, and its square root. Since prime numbers only have two factors (1 and the number itself), the square of a prime number will have exactly 4 divisors. Examples of numbers with only 4 divisors include 4 (2^2), 9 (3^2), 25 (5^2), and so on. **

The divisors of 900 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900. **

Convenient percentages and divisors are numbers that are easy to work with and calculate mentally. For example, percentages like 25%, 50%, and 75% are convenient because they are simple fractions of 100. Divisors like 2, 5, and 10 are also convenient because they are easy to divide by and often result in whole numbers. These convenient percentages and divisors are commonly used in everyday calculations and can help simplify math problems. **