Question

How many prime factors are there in the expression $(12{)}^{43}\times {\left(34\right)}^{48}\times (2{)}^{57}?$

• A. 282
• B. 237
• C. 142
• D. 61

Answer 1

Answer: (A)

282

$\Rightarrow (12{)}^{43}\times (34{)}^{48}\times (2{)}^{57}$
$\Rightarrow (2\times 2\times 3{)}^{43}\times (2\times 17{)}^{48}\times (2{)}^{57}$
$\Rightarrow (2{)}^{43}\times (2{)}^{43}\times (3{)}^{43}\times (2{)}^{48}\times (17{)}^{48}\times (2{)}^{57}$
Hence prime factor $=43+43+43+48+48+57=282$