find-the-highest-power-of-5-contained-in158-

Question Number 48897 by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

f i n d t h e h i g h e s t p o w e r o f 5 c o n t a i n e d i n 158!

Answered by mr W last updated on 29/Nov/18

155 = 31 \times 5

5, 2 \times 5, 3 \times 5, \dots, 31 \times 5 \Rightarrow 31 t i m e s

1 \times 5, 2 \times 5, 3 \times 5, \dots, 6 \times 5 \Rightarrow 6 t i m e s

1 \times 5 \Rightarrow 1 t i m e

t o t a l l y \Rightarrow 38 t i m e s 5 i n 158!

i . e . 5^{38} i s c o n t a i n e d i n 158!

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Nov/18

t h a n k y o u s i r \dots

Answered by rahul 19 last updated on 29/Nov/18

[\frac{158}{5}] + [\frac{158}{25}] + [\frac{158}{125}] = 31 + 6 + 1 = 38

\Rightarrow 5^{38} i s c o n t a i n e d i n 158!

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Nov/18

g o o d \dots t h a n k y o u r a h u l \dots