How many factors does 144 have?

Question

losing2mema · Accepted Answer

Step 1To find the answer, first factor 144 into &#039; factors:      144    =    2    ×    72        =    2    ×    2    ×    36        =    2    ×    2    ×    2    ×    18        =    2    ×    2    ×    2    ×    2    ×    9        =    2    ×    2    ×    2    ×    2    ×    3    ×    3        =          2      4        ×          3      2      Any positive factor of 144 can be expressed as:            2      a        ×          3      b      where       a    =    0    ,    1    ,    2    ,    3    ,    4   and       b    =    0    ,    1    ,    2  That gives 5 possible values for a and 3 possible values for b and therefore      5    ×    3    =    15   factors.Since there are only two distinct &#039;s involved, we can write the factors in a grid with columns for the distinct powers of 2 and rows for the distinct powers of 3:                    1                    2                    4                    8                    16                            3                    6                    12                    24                    48                            9                    18                    36                    72                    144

tinydancer27br · Accepted Answer

Step 1There is another for you to observe      144    =          2      4        ⋅          3      2      5 possibilities to choose             2              0        ~        4            3 possibilities to choose             3              0        ~        2            so            (      4      +      1      )        ⋅          (      2      +      1      )        =    15

How many factors does 144 have?

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