Question

Number of prime factors in $\frac{6^{12}\times (35{)}^{28}\times (15{)}^{16}}{(14{)}^{12}\times (21{)}^{11}}$ is

• A. $56$
• B. $66$
• C. $112$
• D. None of these

Answer 1

The correct option is B $66$

Lets decompose all numbers to their prime factors,

$\frac{\left(2.3{)}^{12}\right(7.5{)}^{28}(3.5{)}^{16}}{\left(2.7{)}^{12}\right(3.7{)}^{11}}$

$=2^{12-12}{.3}^{12+16-11}{.5}^{28+16}{.7}^{28-12-11}$

$=3^{17}{.7}^5{.5}^{44}$

Number of prime facros possible $=$ Sum of all prime powers $=17+5+44=66$