How do I Find Number of Positive Divisors?
Positive divisors refer to the number of whole numbers greater than zero that a number can be divided by without leaving a remainder. For example, the number six has four positive integers because it can be divided by 1, 2, 3 and 6. You may need to find the number of positive divisors if you have a large group of people and want to know how many ways you can split them up into even groups, without anyone left out.
Instructions
1. Complete a prime factorization of the number. Prime factorization means to find the prime numbers that multiplied together will give you the original number. For example, if you were trying to find the number of positive divisors of 360, you would get 2*2*2*3*3*5, or 2^3*3^2*5^1.
2. Isolate the exponents in the prime factorization. Continuing the example, you have 2^3*3^2*5^1, so the exponents would be 3, 2 and 1.
3. Add one to each of the exponents in the prime factorization. In this example, you would add 1 to 3 to get 4, 1 to 2 to get 3 and 1 to 1 to get 2.
4. Multiply the results from step 3 to find the number of positive divisors. Finishing the example, you would multiply 4 times 3 times 2 to find that 360 has 24 positive divisors.
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