How To Find First and Second Non Zero Digits In A Factorial - Hemant Malhotra


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Find last non zero digit of N!

    Represent N = 5a +b form then last non zero digit will be 

    2a! x b!

    Find last non zero digit of 21! 

    21 = 5 x 4 + 1 
    so a = 4 and b = 1

    so last non zero digit =24 x 4! x 1!
    16 x 24 x 1 so last non zero digit = 4

    Find last non zero digit of 34!

    34 = 5 x 6 + 4
    So a = 6 and b = 4 so 26 x 6! x 4!
    Now we need to find the last non zero digit  in 6!  so 6 = 5 x 1 + 1
    so a=1 and b=1
    so 21 x 1! x 1! = 2
    now we know that 6! = 720 so last non zero digit is 2 so no need to do this
    so 26 x 2 x 4!
    27 x 24 = 128 x 24 so last digit=2

    Concept 2 -

    Find last two non zero digits of N!

    Express N = 5a + b then last two non zero digits will be

    12a x a! x (5a + 1)(5a + 2) ... (5a + b)

    EXAMPLE-  find last two non zero digits of 23!

    23 = 5 x 4 + 3
    here a = 4 and b = 3
    so 124 x 4! x (5 x 4 + 1)(5 x 4 + 2) (5 x 4 + 3)
    124 x 4! x 21 x 22 x 23
    now multiple and find last two digits

    NOTE 1 -last two non zero digits of

    5! = 12
    25! = 84
    125! =88

     
    Last non zero digits

    (10!) = 8
    (20!) = 4
    (30!) = 8
    (40!) = 2
    (50!) = 2
    (60!) = 6
    (70!) = 8
    (80!) = 8
    (90!) = 2
    (100!) = 4

    Example- if u want to find last non zero digit of 21!

    You know last non zero digit of 20! is 4
    so 21! = 21 x 20!
    21 x 4 = > 4 is the last non zero digit

     

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