# How many factors does 144 have?

##### 5 Answers

#### Explanation:

Factors of

i.e. in all

#### Explanation:

To find the answer, first factor

#144=2 xx 72#

#=2 xx 2 xx 36#

#=2 xx 2 xx 2 xx 18#

#=2 xx 2 xx 2 xx 2 xx 9#

#=2 xx 2 xx 2 xx 2 xx 3 xx 3#

#=2^4 xx 3^2#

Any positive factor of

#2^a xx 3^b#

where

That gives

Since there are only two distinct primes involved, we can write the factors in a grid with columns for the distinct powers of

it has 15 factors ={ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144}

#### Explanation:

it has 15 factors ={ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144}

15

#### Explanation:

there is another for you to observe @@

5 possibilities to choose

3 possibilities to choose

so

A =

#### Explanation:

The most accurate, yet the most complex method is first, prime decomposing and then using the exponent to calculate how many factors a set number

- Prime decompose the number:

=

=

- Add
#1# to each exponent:

=

=

- Find the products of the exponents:

=

=

Best of luck!