Question
Download Solution PDFFind the number of zeroes in 10 × 20 × 30 × ... × 1000.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
10 × 20 × 30 × ... × 1000
Concept used:
Take 10 as common from each term.
Number of trailing zeroes in n! = Divide n by 5, continue this process until we get the value which is less than 5. Now, all quotients will be added and the resultant number will be the number of zeroes.
Calculations:
10 × 20 × 30 × ... × 1000
⇒ (10 × 1) × (10 × 2) × (10 × 3) × (10 × 4) ..........× (10 × 100)
⇒ 10100 × (1 × 2 × 3 × ... × 100)
⇒ 10100 × (100!)
Number of zeroes = 100 + {(100)/5 + (20)/5}
⇒ 100 + 20 + 4
⇒ 124
∴ The number of trailing zeroes in 10 × 20 × 30 × ... × 1000 is 124.
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