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How can you find the number of positive divisors of a natural number without listing all the divisors?
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.
What else can I help you with?
What are all the positive numbers of 72?
The positive numbers of 72, also known as its positive divisors, are the numbers that can divide 72 without leaving a remainder. These numbers are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. In total, there are 12 positive divisors of 72.
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.
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 the divisers of 42?
The divisors of 42 are the numbers that can divide it without leaving a remainder. These divisors are 1, 2, 3, 6, 7, 14, 21, and 42. Therefore, 42 has a total of eight divisors.
What are all the positive numbers of 72?
The positive numbers of 72, also known as its positive divisors, are the numbers that can divide 72 without leaving a remainder. These numbers are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. In total, there are 12 positive divisors of 72.
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.
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 the divisers of 42?
The divisors of 42 are the numbers that can divide it without leaving a remainder. These divisors are 1, 2, 3, 6, 7, 14, 21, and 42. Therefore, 42 has a total of eight divisors.
What are all the prime numbers between 91 and 100?
The prime numbers between 91 and 100 are 97. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In this case, 97 meets this criteria as it can only be divided by 1 and 97 without leaving a remainder.
What are the divisors of 9?
The divisors of 9 are the numbers that can divide 9 without leaving a remainder. In this case, the divisors of 9 are 1, 3, and 9. This is because 1 multiplied by 9 equals 9, and 3 multiplied by 3 equals 9. Therefore, the divisors of 9 are 1, 3, and 9.
How do I know if 13 is prime?
To determine if 13 is a prime number, check if it has any divisors other than 1 and itself. A prime number is defined as having exactly two distinct positive divisors. Since 13 can only be divided evenly by 1 and 13 without resulting in a fraction, it is indeed a prime number.
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.
What are the divisions of 64?
The divisors of 64 are the numbers that can divide 64 without leaving a remainder. These divisors are 1, 2, 4, 8, 16, 32, and 64. In total, 64 has seven divisors. Additionally, since 64 is a power of 2 (specifically, (2^6)), its divisors are all the powers of 2 up to (2^6).
