what is the least whole number with exactly eleven factors?
To find the least whole number with exactly eleven factors, we need to understand the concept of factors and how to calculate them.
The factors of a number are the whole numbers that divide evenly into that number. For example, the factors of 6 are 1, 2, 3, and 6 because they can divide 6 without leaving a remainder.
To determine the number of factors a whole number has, we need to factorize it. Here are the steps:
1. Start by finding the prime factorization of the number. Prime factorization means breaking down the number into its prime factors (numbers that are only divisible by 1 and themselves). For example, the prime factorization of 12 is 2 x 2 x 3.
2. Next, count the number of times each prime factor appears and add 1 to each exponent. For example, in the prime factorization 2 x 2 x 3, the exponents are 2 and 1. Adding 1 to each exponent gives 3 and 2.
3. Multiply the incremented exponents together. In our example, 3 x 2 is 6.
The result of this multiplication is the number of factors the whole number has.
Now let's apply this method to find the least whole number with exactly eleven factors:
Start with the prime factorization of 11: 11 = 11^1.
Since 11 is a prime number, its only factorization is the number itself raised to the power of 1.
So, using the formula mentioned above, we increment the exponent by 1, giving us (1 + 1) = 2.
Now we have found that the number with exactly eleven factors is 11^2 = 121.
Therefore, the least whole number with exactly eleven factors is 121.