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This is an aspect of number theory but let's start with a rule and a simple example.
If if it just a total number of factors that is required (rather than the values) then this can be obtained by stating the original number in terms of its prime factors.
For example , 100 = 22 x 52.
Add 1 to each exponent and obtain the product : (2 + 1)(2 + 1) = 3 x 3 = 9
Then 100 has 9 factors which are 100, 50, 25, 20, 10, 5, 4, 2, 1.
So for a number to have 100 factors then its prime factors must have exponents of 49 & 1, or 24 & 3, or 19 & 4, or 9 & 9 so that when 1 is added to each exponent the paired product = 100........for example the number generated from, 219 x 34. or from 29 x 39.
Equally 100 = 2 x 2 x 5 x 5 so another number with 100 divisors = 2 x 3 x 54 x 74 And similarly 100 = 4 x 5 x 5 and we can put the exponents in any order so another number with 100 divisors = 24 x 33 x 54. This last number = 270,000.
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What number has exactly 10 divisors?
The first number to have exactly 10 divisors is 48.
What is the smallest number with exactly fourteen divisors?
It is 192.
What number has exactly 1000000 divisors?
1,999,998 has exactly 1,000,000 divisors starting with 1, 2, 4, 6, 8,...up to 1,999,998.
Why 89 is a prime number?
The only numbers which divide into 89 exactly are 1 and 89. These are called factors or divisors. Any number which has exactly 2 divisors (1 and the number itself) is a prime number.
What is the the largest four-digit divisor that has exactly three divisors?
I think you mean, the largest four digit number that has exactly three divisors. 2X3X1663=9,978
What number has exactly 10 divisors?
The first number to have exactly 10 divisors is 48.
How do you find all positive integers N such that the product 2029 x N has exactly three divisors?
There is only 1 value of N that satisfies 2029 x N has exactly three divisors: N = 2029 To have exactly three divisors, the number must be the square of a prime number. 2029 is a prime number with exactly 2 divisors (1 and 2029). Thus the only number with exactly three divisors of which two are 1 and 2029 is 20292 (= 4116841), making N = 2029.
What is the smallest number with exactly fourteen divisors?
It is 192.
What number has exactly 1000000 divisors?
1,999,998 has exactly 1,000,000 divisors starting with 1, 2, 4, 6, 8,...up to 1,999,998.
Why 89 is a prime number?
The only numbers which divide into 89 exactly are 1 and 89. These are called factors or divisors. Any number which has exactly 2 divisors (1 and the number itself) is a prime number.
What is the least whole number with exactly 4 divisors?
6
What is the smallest number with exactly 14 divisors?
The smallest number with exactly 14 divisors is 192. The divisors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192 itself.
What is the the largest four-digit divisor that has exactly three divisors?
I think you mean, the largest four digit number that has exactly three divisors. 2X3X1663=9,978
What is the least whole number with exactly four positive divisors?
It is 6.
What is the smallest whole number that has exactly 4 positive divisors?
I guess that would be the number 6.
Is the smallest number with 100 divisors 45360?
Yes.
Why is 100 a abundent number?
Because the sum of its proper divisors is greater than 100.
