Question

Find the maximum value of λ such that 18^λ divides 28!​

Answer 1

Answer:

For that, perform the following calculation:

[all divisions are integral]

157/3=52

52/3=17

17/3=5

5/3=1

1/3=0 [until quotient is 0 ]

adding all the quotients = 75

Thus, 375∣157! or 975/2=937∣157!

Thus 1837∣157!

Answer 2

Answer:

prime factors of 18 = 3^2 × 2

exponents of 3 = [28/3] + [28/3^2] + [28/3^3] = 9 + 3 + 1 = 13

exponents of 3^2 = 6

so value of lambda = 6