Question

How many prime factors are there in the expression (12)⁴³ × (34)⁴⁸ × (2)⁵⁷? 

(a) 282

(b) 237 

(c) 142 

(d) 61

Answer 1

The answer is: (a) 282

Answer 2

Correct option : (a) 282

\(12^{43} \times 34^{48} \times 2^{57}=(3\times 2^2)^{43} \times (2\times 17)^{48} \times 2^{57}\)

\(=2^{86+48+57}\times3^{43}\times 17^{48}\)

\(=2^{191}\times 3^{43}\times17^{48}\)

& Number of prime factors = 191 + 43 + 48 = 282.