Question

Find number of zeros in 1^1*2^2*3^3*....48^48*49^49?

Answer 1

Answer:

250 Zeroes will be There

Step-by-step explanation:

Find number of zeros in 1^1*2^2*3^3*....48^48*49^49

Number of Zeroes Will Depend on Multiplying by 10

10 = 2 * 5

Lets find  5  &  10

as 2 Will be much more than 5 as

5⁵  -  5 times 5

15¹⁵ - (5 * 3)⁵  -  15 times 5

25₂⁵ - (5 * 5)²⁵ -  50 times 5

35³⁵ - (5 *7)³⁵ - 35 Times 5

45⁴⁵ - (5 *9)⁴⁵ - 45 Time 5

= 150 Times 5

48⁴⁸ = (2 * 2 * 2 * 2 * 3)⁴⁸  = 4*48 = 192 times 2 so Need not to check as only 150 times 5 is there

2 * 5 = 10  => 150 times 10

10¹⁰  - (10 * 1)¹⁰   -   10 Time 10

20²⁰  - (10 * 2)²⁰   -  20 Time 10

30³⁰  - (10 * 3)³⁰   -   30 Time 10

40⁴⁰  - (10 * 4)⁴⁰   -   40 Time 10

10 + 20 + 30 + 40 = 100 time s 10

10¹⁵⁰ * 10¹⁰⁰ = 10²⁵⁰

=> 250 Zeroes will be There