Question

How many numbers less than 100 have exactly 11 factors? EXPLAIN.​

Answer 1

Explanation:

There are infinite numbers with 11 factors. I believe you wanted to ask what is the smallest number with exactly 11 prime factors. In mathematics, questions can mean different things if the right words are not used. To get the number you are looking for get a sequence of 11 prime numbers starting from the smallest 2, i.e 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. Then multiply 2x3x5x7x…x31

Answer 2

0 numbers

Explanation:

The number of factors of a number is given by the formula:

`\sf (a + 1)(b + 1)`

where a is the highest power of 2 that divides the number and b is the highest power of 3 that divides the number.

We want a number less than 100 with exactly 11 factors.

So, we want.

`\sf (a + 1)(b + 1) = 11`

We can factor 11 as 1*11. So, we need a + 1 = 1 and b + 1 = 11.

Solving for a and b, we get a = 0 and b = 10.

However, there are no numbers less than 100 that are divisible by 10 only. The smallest number divisible by 10 is 10.

Therefore, there are 0 numbers less than 100 with exactly 11 factors.