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# A number that is greater than one whose only divisors equal one and itself?

Updated: 9/16/2023

Wiki User

14y ago

That is called a Prime number.

Wiki User

14y ago

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Q: A number that is greater than one whose only divisors equal one and itself?
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### What is a perfect number and give an example of one?

A perfect number is equal to the sum of its proper divisors (the factors excluding the number itself.) 6 is a perfect number. Its proper divisors are 1, 2 and 3.

### What is the term for equal to the sum of its proper factors?

A perfect number is the term for a number that is equal to the sum of its proper divisors. Be careful not to confuse that with proper factors. Proper divisors include 1 but not the number itself. Proper factors don't include either I or the original number.

### What is an amicable number?

An amicable number is one of a pair of numbers which have the property that the sum of the divisors of each, excluding itself, is equal to the other number.

### What are the perfection numbers?

A number is considered perfect if it is equal to the sum of all its positive factors/divisors, excluding itself. These are the first few perfect numbers: * 6 * 28 * 496 * 8128 * 33550336 * 8589869056A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. An example 1+2+3=6 and 1x2x3=6

### Why 21 is not a perfect number?

First, you want to know the definition of a perfect number: A perfect number is an integer which is equal to the sum of all its positive integer divisors that are less than itself. Example: The positive integer divisors of 6, less than 6, are 1, 2, and 3. The sum of those divisors is 1 + 2 + 3 = 6. Therefore, 6 is a perfect number. Now, 21 does not meet this definition and therefore is not a perfect number. Let's try it. There are three positive divisors of 21, namely, 1, 3, and 7, that are less than 21, itself. (There are no others.) But the sum of these divisors is 1 + 3 + 7 = 11, which is not equal to 21. Therefore, we confirm that 21 is not a perfect number.

### Why are perfect numbers perfect?

A perfect number is only classified as a perfect number because all of its proper divisors add up to itself. For example, the proper divisors of six are one, two and three. Those numbers added together equal six. Therefore, six is a perfect number.

### When is the absolute value of a number equal ti itself?

When the number is greater than or equal to zero. e.g. l 5 l = 5

### What numbers have exactly 3 divisors?

An integer (call it 'x') has exactly 3 divisors if and only if it is the square of a prime number. In other words, to generate a list of integers with exactly 3 divisors, just keep squaring prime numbers. A number with 3 divisors cannot be prime (a prime number has only 2 divisors, 1 and itself). So it must be a composite number, which is a number that can be factored as a product of prime numbers (Fundamental Theorem of Arithmetic) -- i.e. a composite number must have at least one prime divisor. In the case where the number has only 3 divisors, two of them are 1 and the number itself (neither of which are prime). Therefore the third divisor must be a prime number. So the three divisors of 'x' are: 1, p, x where p is prime. Now since p is a divisor (or factor) of x, and the only other divisor besides 1 and x itself, x must equal p*p -- or x=p^2 . Obvious x can't equal p*x and if x = p*1, x=p so x is prime, or has only 2 divisors... If x = p^(3) , then x = p*p* p , or p*(p^2) ... this means that p^2 would also have to be a divisor of x, and this would contradict with x having only 3 divisors. For the same reason, x = p^(greater than 3) is also not possible. So the only possibility is that an integer with exactly 3 divisors is the square of a prime number "p". The divisors are 1, p, and p^2. I'm sure there's a simpler, more elegant way of explaining this, but it should be clear enough.

### When the absolute value of a number equal to itself?

When the number is greater than or equal to zero. e.g. l 5 l = 5

### What is 29.47 equals?

This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.

### What is the reflective property?

That means that in the relation considered, any object relates to itself: For any "x", relation(x, x) is true. For example, this is a property of equality (any number is equal to itself), of congruence (any object is congruent to itself), and to relationships such as greater-than-or-equal (any number is greater than or equal to itself) and the non-strict subset relation (any set is a subset of itself).

### When is the absolute value of a number equal to itself?

The absolute value of a number equals the number itself if and only if the number is a positive real number (x &gt;= 0 and does not include a nonzero imaginary component).