Find the number of zeroes in 10 x 20 x 30x……x 1000.

Created: 8 months ago | Updated: 3 months ago
Job Solution Bangladesh Bank সমন্বিত ৮ ব্যাংক ও ১ টি আর্থিক প্রতিষ্ঠান || সিনিয়র অফিসার (সাধারণ) (20-01-2023) গণিত
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Concept:

Take 10 as common form each term.

Number of trailing zeroes in n! = divide n by 5 and all the quotients till it reaches less than 5. 

Calculations:

10 x 20 x 30 x …… x 1000

= (10 x 1) x (10 x2) x (10 x 3) x ………………… x (10 x 1000)

= 10100 x (1 x 2 x 3 x …………… x 100)

= 10100 x 100!

Number of zeroes = 100 + 100/5 + 100/52

                               = 100 + 20 + 4

                               = 124

1 year ago
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