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How many ordered triples of pairwise distinct, positive integers (a,b,c) are there such that abc=10^6?

  • maths -

    10^6 = (2x5)^6
    = (2^6)(5^6)

    Possible cases:
    1x64x15628 --- arrange in 6 ways
    2x32x15625 --- arrange in 6 ways
    4x16x15625 --- 6 more
    8x8x15625 --- arrange in 3 ways
    64x5x3125 ---- 6 ways
    64x25x625 ----- 6 ways
    64x125x125 ---- 3 ways

    I count 36 of them

    check my logic to make sure I didn't miss any

    e.g. for 64x25x625 we could have
    (64,25,625) , (64,625,25) , (25,64,625), (25,625,64), (625,25,64), (625,64,25)

  • maths -

    false

  • maths -

    Do ur hw ur self .....

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