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In how many possible ways can you write 1800 as a product of 3 positive integers a, b and c.

the Prime Factors of 1800 = 2 X 2 X 2 X3 X3 X 5 X 5

  • ( 3-1 ) (2) ways and by permutation we have:5!/2!(5-2)! This gives:5*4*3!/2*1*3!=10ways.
  • (3-1 ) ( 2) and by permutation,we have:4*3*2*1/2*2=6ways
  • (3-1 ) (2) and by permutation we have 4*3*2*1/2*2=6ways.

To get the total number of ways 1800 can be written as a product of 3 integers we get the product of ways it’s prime factors can be written. That is:10*6*6=360

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