KVPY2015MathematicsPermutation and Combination
The largest non-negative integer k such that 24^ k divides 13 ! is.
Options
- A2
- B3
- C4
- D5
Correct answer
B. 3
Step-by-step solution
24^ k (2³ 3 )^ k Exponent of 2 in 13! [ 13 2 ]+ [ 13 2² ]+ [ 13 2³ ]=10 Exponent of 3 in 13 ! [ 13 3 ]+ [ 13 3² ]=5 So (2³ 3 )³ So K =3