## How do you find the sum of the proper divisors of a number?

∑ d ∣ n d = ∏ i = 1 k p i m i + 1 – 1 p i – 1 . If we want only proper divisors, we should not include n in the sum, so we obtain the formula for proper divisors by subtracting n from our formula. (24−12−1)(33−13−1)(53−15−1)=15⋅26⋅1242⋅4=6045….Proof.

Title | formula for sum of divisors |
---|---|

Classification | msc 11A05 |

**What is the sum of all the divisors?**

The formula for finding the sum of divisors is given as: Sum of divisors =(P0+P1+P2…… Pa)(q0+q1+q2……qb)(r0+r1+r2…… rc) .

**What is proper divisor?**

A positive proper divisor is a positive divisor of a number , excluding itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number of proper divisors of is therefore given by. where is the divisor function.

### How do you find the sum of the divisors of 8064?

The sum of these divisors (counting 8,064) is 26,520, the average is 55,2.5….Divisors of 8064.

Even divisors | 42 |
---|---|

4k+3 divisors | 3 |

**What is the sum of divisors of 360?**

Solution : The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. ∴ the sum of all odd proper divisors of 360 is 78.

**How do you find the sum of the divisors of a number in Python?**

Python Math: Returns sum of all divisors of a number

- Sample Solution:-
- Python Code: def sum_div(number): divisors = [1] for i in range(2, number): if (number % i)==0: divisors.append(i) return sum(divisors) print(sum_div(8)) print(sum_div(12))
- Pictorial Presentation:
- Flowchart:
- Python Code Editor:

## How do you find the number of divisors of 1420?

1420 contains number of terms = 3 × 2 × 2 = 12; Then, the number of factors or divisors = 12.

**What is the sum of divisors of 18?**

39

Hence, the sum of the divisors of 18 is 39.

**What are the proper divisors of 60?**

1 to 100

n | Divisors | σ(n) |
---|---|---|

59 | 1, 59 | 60 |

60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 168 |

n | Divisors | σ(n) |

61 | 1, 61 | 62 |

### What are the proper divisors of 12?

Example: 12 has for divisors 6, 4, 3, 2 and 1.

**What is the sum of all divisors of 133?**

The number 133 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 133) is 160, the average is 40.

**What is the sum of all proper divisors of a number?**

Given a natural number, calculate sum of all its proper divisors. A proper divisor of a natural number is the divisor that is strictly less than the number. For example, number 20 has 5 proper divisors: 1, 2, 4, 5, 10, and the divisor summation is: 1 + 2 + 4 + 5 + 10 = 22. Attention reader! Don’t stop learning now.

## How do you find the sum of divisors of nequals?

Theorem 1. Suppose that nis a positive integerwhose factorization into prime factorsis ∏i=1kpimi, where the pi’s are distinct primes and the multiplicitiesmiare all at least 1. Then the sum of the divisors of nequals

**How do you find all the divisors of N?**

All the divisors of n can be expressed as p 1a x p 2b x …, where 0 <= a <= k1 and 0 <= b <= k2. (p 10 x p 2k2) + (p 11 x p 2k2) +……+ (p 1k1 x p 2k2 ).

**How do you find the sum of all divisors of an array?**

So, given a number n, by prime factorization we can find the sum of divisors of all the divisors. But in this problem we are given that n is product of element of array. So, find prime factorization of each element and by using the fact a b x a c = a b+c.