Find the number of zeroes in 10 × 20 × 30 × ... × 1000.

  1. 100
  2. 124
  3. 120
  4. 150

Answer (Detailed Solution Below)

Option 2 : 124
Free
RRB NTPC CBT-I Official Paper (Held On: 4 Jan 2021 Shift 1)
5.4 Lakh Users
100 Questions 100 Marks 90 Mins

Detailed Solution

Download Solution PDF

Given:

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.

Latest RRB NTPC Updates

Last updated on Jun 9, 2025

-> RRB NTPC 2025 Exam Postponed. Railway Recruitment Board has rescheduled the RRB NTPC Exam for June 5, 2025 (Shift 3). 

-> RRB NTPC Exam Analysis 2025 is LIVE now. All the candidates appearing for the RRB NTPC Exam 2025 can check the complete exam analysis to strategize their preparation accordingly. 

-> The RRB NTPC Admit Card 2025 has been released on its official website.

-> Candidates who will appear for the RRB NTPC Exam can check their RRB NTPC Time Table 2025 from here.

-> The RRB NTPC CBT 1 Exam is scheduled from 5th June to 24th June 2025 as per the revised tentative exam schedule. 

-> The RRB NTPC 2025 Notification has been released for a total of 11558 vacancies.

-> A total of 3445 Vacancies have been announced for Undergraduate posts like Commercial Cum Ticket Clerk, Accounts Clerk Cum Typist, Junior Clerk cum Typist & Trains Clerk.

-> A total of 8114 vacancies are announced for Graduate-level posts in the Non-Technical Popular Categories (NTPC) such as Junior Clerk cum Typist, Accounts Clerk cum Typist, Station Master, etc.

-> Prepare for the exam using RRB NTPC Previous Year Papers.

-> Check out the Rajasthan PTET Admit Card 2025 and UPSC Prelims Result Date 2025 here.

More Quick Math Questions

Get Free Access Now
Hot Links: teen patti master golden india teen patti master master teen patti