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What are the divisors of 543?
Oh, isn't that a happy little question! The divisors of 543 are the numbers that can divide evenly into it without leaving a remainder. In this case, the divisors of 543 are 1, 3, 181, and 543. Just like in painting, each divisor plays a special role in creating a beautiful masterpiece of numbers.
What are the divisors of 11?
Since 11 is a prime number, its only divisors are 1 and itself.
What is the greatest common divisor of 132?
You need at least two numbers to find a GCF.
What has excatly 3 factors?
Squares of prime numbers are the only numbers with three factors, since there must be only one nontrivial divisor for a number to have three factors. That number must thus be prime.
What number only have three factors?
squares of prime numbers
What Numbers that go into 113?
The numbers that go into 113 are its divisors. Since 113 is a prime number, it has only two divisors: 1 and 113 itself. Therefore, the only numbers that divide evenly into 113 are 1 and 113.
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.
What numbers can go into 149?
The numbers that can go into 149 are its divisors. Since 149 is a prime number, its only positive divisors are 1 and 149 itself. Therefore, the numbers that can divide 149 without leaving a remainder are 1 and 149.
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 divisor of 7?
The divisors of 7 are the numbers that can divide 7 without leaving a remainder. Since 7 is a prime number, its only divisors are 1 and 7 itself. Therefore, the divisors of 7 are 1 and 7.
Which numbers go into 59?
59 is a prime number. 1 and 59 are the only divisors of 59.
What numbers go into both 15 and 70?
The numbers that go into both 15 and 70 are their common divisors. The divisors of 15 are 1, 3, 5, and 15, while the divisors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The only common divisors between the two sets are 1 and 5. Therefore, the numbers that go into both 15 and 70 are 1 and 5.
What goes into 14 and 20?
The numbers that go into both 14 and 20 are called common divisors. The common divisors of 14 are 1, 2, 7, and 14, while the common divisors of 20 are 1, 2, 4, 5, 10, and 20. The only common divisors between the two numbers are 1 and 2. Therefore, 1 and 2 are the numbers that go into both 14 and 20.
Why does 1 not count as a prime number?
Prime numbers have two and only two divisors. The number 1 only has one.
Which of the numbers 31 41 51 and 61 is a composite number?
A composite number is a positive integer greater than 1 that has more than two distinct positive divisors. In this case, the number 51 is a composite number because it has divisors other than 1 and itself, such as 3 and 17. Numbers 31, 41, and 61 are all prime numbers, as they only have two distinct positive divisors, 1 and the number itself.
Are all prime numbers imperfect?
yes. The only divisors of a prime number are itself and 1. Without counting the prime number, the sum of it's divisors is always 1.
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.
