Find a number between 20 and 30 that is half the sum of its factors

Are we counting either 1 or the number itself as factors

e.g. - are the factors of 10
just 2,5 or 1,2,5,10 ?

To find a number that is half the sum of its factors between 20 and 30, we can start by listing the factors of each number in that range.

Factors of 20: 1, 2, 4, 5, 10, 20
Sum of factors of 20: 1 + 2 + 4 + 5 + 10 + 20 = 42

Factors of 21: 1, 3, 7, 21
Sum of factors of 21: 1 + 3 + 7 + 21 = 32

Factors of 22: 1, 2, 11, 22
Sum of factors of 22: 1 + 2 + 11 + 22 = 36

Factors of 23: 1, 23
Sum of factors of 23: 1 + 23 = 24

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Sum of factors of 24: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60

Factors of 25: 1, 5, 25
Sum of factors of 25: 1 + 5 + 25 = 31

Factors of 26: 1, 2, 13, 26
Sum of factors of 26: 1 + 2 + 13 + 26 = 42

Factors of 27: 1, 3, 9, 27
Sum of factors of 27: 1 + 3 + 9 + 27 = 40

Factors of 28: 1, 2, 4, 7, 14, 28
Sum of factors of 28: 1 + 2 + 4 + 7 + 14 + 28 = 56

Factors of 29: 1, 29
Sum of factors of 29: 1 + 29 = 30

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Sum of factors of 30: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72

Now, let's identify the number between 20 and 30 that is half the sum of its factors. From the calculations, we can see that the number 23 has a sum of factors equal to 24, which is half of 48. Therefore, 23 is the number between 20 and 30 that satisfies the given condition.

To find a number between 20 and 30 that is half the sum of its factors, let's break down the steps:

1. Identify the factors of the numbers between 20 and 30, inclusive.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 21: 1, 3, 7, 21
Factors of 22: 1, 2, 11, 22
Factors of 23: 1, 23
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 25: 1, 5, 25
Factors of 26: 1, 2, 13, 26
Factors of 27: 1, 3, 9, 27
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 29: 1, 29
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

2. Calculate the sum of the factors for each number.
Sum of factors of 20: 1 + 2 + 4 + 5 + 10 + 20 = 42
Sum of factors of 21: 1 + 3 + 7 + 21 = 32
Sum of factors of 22: 1 + 2 + 11 + 22 = 36
Sum of factors of 23: 1 + 23 = 24
Sum of factors of 24: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
Sum of factors of 25: 1 + 5 + 25 = 31
Sum of factors of 26: 1 + 2 + 13 + 26 = 42
Sum of factors of 27: 1 + 3 + 9 + 27 = 40
Sum of factors of 28: 1 + 2 + 4 + 7 + 14 + 28 = 56
Sum of factors of 29: 1 + 29 = 30
Sum of factors of 30: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72

3. Compare the sum of the factors to half of the number.
For the number 20, half of the sum of its factors (42/2) is 21, which is not between 20 and 30.
For the number 21, half of the sum of its factors (32/2) is 16, which is not between 20 and 30.
For the number 22, half of the sum of its factors (36/2) is 18, which is not between 20 and 30.
For the number 23, half of the sum of its factors (24/2) is 12, which is not between 20 and 30.
For the number 24, half of the sum of its factors (60/2) is 30, which is between 20 and 30.
For the number 25, half of the sum of its factors (31/2) is 15.5, which is not between 20 and 30.
For the number 26, half of the sum of its factors (42/2) is 21, which is not between 20 and 30.
For the number 27, half of the sum of its factors (40/2) is 20, which is not between 20 and 30.
For the number 28, half of the sum of its factors (56/2) is 28, which is not between 20 and 30.
For the number 29, half of the sum of its factors (30/2) is 15, which is not between 20 and 30.
For the number 30, half of the sum of its factors (72/2) is 36, which is not between 20 and 30.

Based on the analysis above, we can see that there is only one number between 20 and 30 that is half the sum of its factors, which is 24.