Show all factor pairs, prime factorization (factor tree), sum of factors (divisors), aliquot sum, and prime power decomposition of 36.

We do this by listing out all pairs of numbers greater than 0 and less than or equal to 36 who have a product equal to 36:

Number | Factor Pairs | Factor Pairs Sum |
---|

36 | 1 x 36 | 37 |

36 | 2 x 18 | 20 |

36 | 3 x 12 | 15 |

36 | 4 x 9 | 13 |

36 | 6 x 6 | 12 |

There are 5 factor pairs of 36.

__List factors of 36__

1, 2, 3, 4, 6, 9, 12, 18, 36

__List odd factors of 36__

1, 3, 9

__List even factors of 36__

2, 4, 6, 12, 18, 36

__Calculate proper factors of 36__

Proper factors are all factors except for the number itself, in this case 36

1, 2, 3, 4, 6, 9, 12, 18

Now, show the prime factorization (factor tree) for 36 by expressing it as the product of ALL prime numbers.

36 = 2 x 18 <--- 2 is a prime number

Next step is to reduce 18 to the product of prime numbers:

18 = 3 x 6 <--- 3 is a prime number

Next step is to reduce 6 to the product of prime numbers:

6 = 2 x 3 <--- 2 is a prime number

Next step is to reduce 3 to the product of prime numbers:

__Our prime factorization (factor tree) is as follows:__

**2 x 2 x 3 x 3**__Show the Prime Power Decomposition (Group Common Terms)__

**2**^{2} x 3^{2}__Show the sum of factors (divisors) for 36__

1 + 36 + 2 + 18 + 3 + 12 + 4 + 9 + 6 =

**91**__Show the aliquot sum:__

The aliquot sum is the sum of all the factors of a number except the number itself

1 + 2 + 18 + 3 + 12 + 4 + 9 + 6 =

**55**[+] __Watch the Factorization Video__