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Which number has the smallest number of divisors?
In fact 120 is the smallest number having 16 divisors.
How do you find the N divisors of a number?
Let d( n ) be the number of divisors for the natural number, n . We begin by writing the number as a product of prime factors: n = p a q b r c then the number of divisors, d( n ) = ( a +1)( b +1)( c +1)… To prove this, we first consider numbers of the form, n = p a .
What are the divisors of N?
The proper divisors of the integer n are the positive divisors of n other than n itself. The proper divisors of 27 are 1, 3 and 9. Prime numbers are those integers greater than one whose only divisors are one and themselves (so whose only proper positive divisor is one).
How do you find the smallest integer?
2 Answers. x=0 is the smallest integer.
What is the smallest number with exactly 14 divisors?
192
Hence 192 is the smallest integer that has exactly 14 divisors.
What is the smallest number that has 8 divisors?
24
with one exception. The smallest number with 8 divisors would be 30 = 2*3*5 if the theorem always held, but in fact the smallest number with 8 divisors is 24.
What is the smallest number with exactly 10 divisors?
The required smallest number with 10 different factors is 72.
What are the divisors of 8?
Divisors of numbers
| Number | Prime factorization | Divisors |
|---|---|---|
| 6 | 2 * 3 | 1, 2, 3, 6 |
| 7 | 7 | 1, 7 |
| 8 | 23 | 1, 2, 4, 8 |
| 9 | 32 | 1, 3, 9 |
What is the number of divisors of 360?
The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, making a total of 24 divisors.
What is the divisors of 1?
whose only proper divisor is 1 is called a prime number. Equivalently, a prime number is a positive integer that has exactly two positive factors: 1 and itself.
How many divisors does 1 have?
1 is a special case for almost everything. In this case, because it is the only natural number with no proper divisors, just as your definition implies. General rule with number theory: 1 is always weird.