[administration]

Q. A number has 144 factors, then what is the maximum number of ways in which it can be written as product of two co-prime factors??
a) 16
b) 24
c) 32
d) 48

e) 64

asked by Hemant Yadav

[Wonder Boy]

since 144 is the total no. of factors so 144= 2x2x2x2x3x3 ..so total of 6 prime factors… Now no. of co-prime factors = 6c0 + 6c1+ 6c2 + 6c3 + 6 c4 + 6c5 + 6c6 = 64 which consist of similar terms so we divide it by 2 so total required term = 64/2 =32

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