Show Factorization for 75

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Show all factor pairs, prime factorization (factor tree), sum of factors (divisors), aliquot sum, and prime power decomposition of 75.

We do this by listing out all pairs of numbers greater than 0 and less than or equal to 75 who have a product equal to 75:
75 = 1 x 75
75 = 3 x 25
75 = 5 x 15

There are 3 factor pairs of 75.

List factors of 75
1, 3, 5, 15, 25, 75

List odd factors of 75
1, 3, 5, 15, 25, 75

List even factors of 75


Calculate proper factors of 75
Proper factors are all factors except for the number itself, in this case 75
1, 3, 5, 15, 25

Now, show the prime factorization (factor tree) for 75 by expressing it as the product of ALL prime numbers.
75 = 3 x 25 <--- 3 is a prime number

Next step is to reduce 25 to the product of prime numbers:
25 = 5 x 5 <--- 5 is a prime number

Next step is to reduce 5 to the product of prime numbers:
Our prime factorization (factor tree) is as follows:
3 x 5 x 5

Show the Prime Power Decomposition (Group Common Terms)
3 x 52

Show the sum of factors (divisors) for 75
1 + 75 + 3 + 25 + 5 + 15 = 124

Show the aliquot sum:
The aliquot sum is the sum of all the factors of a number except the number itself
1 + 3 + 25 + 5 + 15 = 49