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Answer

↓Steps Explained:↓

Show all factor pairs, prime factorization,

sum of factors (divisors), aliquot sum,

and prime power decomposition of 50

Factor Pair Logic Rules

1) 0 < Factor Pairs ≤ 50

2) The factor pair product = 50

Factor Pairs Table

Number	Factor Pairs	Factor Pairs Sum
50	1 x 50	51
50	2 x 25	27
50	5 x 10	15

There are 3 factor pairs of 50

List factors of 50 also known as τ(50)

1, 2, 5, 10, 25, 50

τ(50) = 6

List odd factors of 50

1, 5, 25

List even factors of 50

2, 10, 50

Calculate proper factors of 50

Proper factors are all factors except for the number itself
in this case 50

1, 2, 5, 10, 25

Prime factorization for 50

50 = 2 x 25 <--- 2 is a prime number

Reduce 25 to the product of primes:

25 = 5 x 5 <--- 5 is a prime number

Reduce 5 to the product of primes:

Show prime factorization:

2 x 5 x 5

Prime Power Decomposition

2 x 5²

Show the sum of factors (divisors) for 50

1 + 50 + 2 + 25 + 5 + 10 = 93

Show the aliquot sum:

This is the sum of all the factors except the number

1 + 2 + 25 + 5 + 10 = 43

Final Answer