Factors.

First of all find the factor tree of the given number which is as follows :

2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 17 x 17 = $2^{6}$ x $3^{4}$ x $17^{2}$ =1498176

Now , its very simple ..... just add one (1) to all the powers and multiply them and this rule is followed by every number . Sorry but i don't have the proof for this method.

Therefore, number of factors = * ( 6 + 1 ) x ( 4 + 1 ) x ( 2 + 1 ) = 7 x 5 x 3 = 35 x 3 * = * $\boxed{105}$ factors... *

CHEERS !!!!!!

105

euler's formula

by factorising it we get

2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 17 x 17 =1498176

no of factors =7 5 3=105

question is asking the factors not prime factors so the factors of 1498176 are 105