# Show Factorization for 42

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Show all factor pairs, prime factorization (factor tree), sum of factors (divisors), aliquot sum, and prime power decomposition of 42.

We do this by listing out all pairs of numbers greater than 0 and less than or equal to 42 who have a product equal to 42:
42 = 1 x 42
42 = 2 x 21
42 = 3 x 14
42 = 6 x 7

There are 4 factor pairs of 42.

List factors of 42
1, 2, 3, 6, 7, 14, 21, 42

List odd factors of 42
1, 3, 7, 21

List even factors of 42
2, 6, 14, 42

Calculate proper factors of 42
Proper factors are all factors except for the number itself, in this case 42
1, 2, 3, 6, 7, 14, 21

Now, show the prime factorization (factor tree) for 42 by expressing it as the product of ALL prime numbers.
42 = 2 x 21 <--- 2 is a prime number

Next step is to reduce 21 to the product of prime numbers:
21 = 3 x 7 <--- 3 is a prime number

Next step is to reduce 7 to the product of prime numbers:
Our prime factorization (factor tree) is as follows:
2 x 3 x 7

No prime power decomposition exists since there are no duplicate prime numbers in the prime factorization:

Show the sum of factors (divisors) for 42
1 + 42 + 2 + 21 + 3 + 14 + 6 + 7 = 96

Show the aliquot sum:
The aliquot sum is the sum of all the factors of a number except the number itself
1 + 2 + 21 + 3 + 14 + 6 + 7 = 54