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How can you find the number of positive divisors of a natural number without listing all the divisors?
Wiki User
∙ 13y ago
What you are trying to do is called the tau function - the number of positive divisors of a natural number, n, is written as tau(n). How to do it:
Simplify your number into its prime factors.
For example, 84 = 4 * 3 * 7 = (2^2) * (3^1) * (7^1).
Then, make a list of all the powers from the previous step. This gives us a list of 2, 1, and 1.
Add one to every number in the list. Our list is now 3, 2, and 2.
Multiply all the numbers in the list together, and you're done. 3 * 2 * 2 = 12.
84 has 12 positive divisors, which is easily verified:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
Wiki User
∙ 13y ago
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Is 0.865 a natural number?
No. Natural numbers are positive (or zero) whole numbers - without digits after the decimal point.
Why do you have to learn about greatest common divisors?
In math, the greatest common divisor (GCD) of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
1 is part of whole number natural nubmer?
A whole number is one without a decimal or fraction, and a natural number is any positive integer, so this is both a whole number and an integer.
What is a prime number maths related?
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number cannot be divided evenly (without a remainder) by any other number except 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.
A positive number without fractions or decimals?
An example of a positive number without fractions or decimals is the whole number 7.
What is positive external financing?
Positive external financing is creates a money source for the organization without getting them into significant debt. Listing shares on the stock market is positive external financing.
Why do you have to learn about greatest common divisors?
In math, the greatest common divisor (GCD) of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
Is 0.865 a natural number?
No. Natural numbers are positive (or zero) whole numbers - without digits after the decimal point.
What are all the divisors of 12?
12, 6, 4, 3, 2, and 1 are the divisors of 12 because these numbers divide 12 without leaving any remainder.
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.
Are factors of a number also divisors of the number?
n mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder. That is to say factors and divisors are the exact same thing.
What is the Lcm of 12 and 8 without listing?
24
1 is part of whole number natural nubmer?
A whole number is one without a decimal or fraction, and a natural number is any positive integer, so this is both a whole number and an integer.
I don't understand how to do integers?
Integers are the natural numbers (positive and negative) that can be written without a decimal or a fraction attached.see en.wikipedia.org/wiki/Integer
How many swear words are in the world without listing them?
a lot
What are the factors of -228?
I assume that we are speaking entirely of positive integers. There are six divisors of 228 that are less than 15: 1, 2, 3, 4, 6, and 12. There are six divisors of 228, greater than 15: 19, 38, 57, 76, 114, and 228 itself. There are several convenient ways to check that you have got them all, without the labour of dividing the first 228 integers into 228. One way is the following: Note, first, that 228 = 19 X 12 = 19 X 3 X 2 X 2. We may call that its 'prime factorisation'. Because every positive integer can be factorised into positive prime integers in only one way, we may safely conclude that every positive divisor of 228 must contain 19, either once or not at all; similarly, it must contain 3 once or not at all; and it must contain 2, twice, once, or not at all. That allows 2 X 2 X 3 = 12 choices for a divisor of 228; hence, there must be twelve divisors of 228, including, of course, 1 and 228 itself. Now, half of these divisors must be less than the square-root of 228, which is just a little bit more than 15; half must be more than 15. 228 is not a perfect square, so we may conclude that six divisors are less than 15. They are easy to identify, since their divisors, in turn, must contain some combination of 1's, 2's and 3's. The remaining six divisors, greater than 15, can be found by dividing the first six divisors into 228. And the job is done. If you want negative divisors, simply take the negatives of all the twelve positive divisors. canislunis
Is -45 a natural number?
Yes. Natural numbers simply mean anything that is natural (or in simpler terms, any positive number without decimals, excluding 0, unless you say there is -12 or 0.4 of a person in a room)
