Factorization Calculator

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Show all factor pairs, prime factorization (factor tree), sum of factors (divisors), aliquot sum, and prime power decomposition of 465.

We do this by listing out all pairs of numbers greater than 0 and less than or equal to 465 who have a product equal to 465:
465 = 1 x 465
465 = 3 x 155
465 = 5 x 93
465 = 15 x 31

There are 4 factor pairs of 465.

List factors of 465
1, 3, 5, 15, 31, 93, 155, 465

List odd factors of 465
1, 3, 5, 15, 31, 93, 155, 465

List even factors of 465


Calculate proper factors of 465
Proper factors are all factors except for the number itself, in this case 465
1, 3, 5, 15, 31, 93, 155

Now, show the prime factorization (factor tree) for 465 by expressing it as the product of ALL prime numbers.
465 = 3 x 155 <--- 3 is a prime number

Next step is to reduce 155 to the product of prime numbers:
155 = 5 x 31 <--- 5 is a prime number

Next step is to reduce 31 to the product of prime numbers:
Our prime factorization (factor tree) is as follows:
3 x 5 x 31

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

Show the sum of factors (divisors) for 465
1 + 465 + 3 + 155 + 5 + 93 + 15 + 31 = 768

Show the aliquot sum:
The aliquot sum is the sum of all the factors of a number except the number itself
1 + 3 + 155 + 5 + 93 + 15 + 31 = 303