isi-entrance 2011 Q5

isi-entrance · India · solved Number Theory Divisibility and Divisor Analysis

Among all the factors of $4 ^ { 6 } 6 ^ { 7 } 21 ^ { 8 }$, the number of factors which are perfect squares is
(a) 240
(b) 360
(c) 400
(d) 640

(C) Now, $4 ^ { 6 } 6 ^ { 7 } 21 ^ { 8 } = 2 ^ { 19 } 3 ^ { 15 } 7 ^ { 8 }$. There are 9 even exponents available for power of 2, 7 for power of 3, and 4 for power of 7. Total perfect square factors $= 252 + 63 + 28 + 36 + 9 + 7 + 4 + 1 = 400$.

Among all the factors of $4 ^ { 6 } 6 ^ { 7 } 21 ^ { 8 }$, the number of factors which are perfect squares is\\
(a) 240\\
(b) 360\\
(c) 400\\
(d) 640

Paper Questions

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