Question

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

Answer 1

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)

Answer 2

false

Answer 3

Do ur hw ur self .....