Modulus & Division: Last Digit of Numbers Explained

[Rishav sapahi]

Isn't it amusing ?What could be the probable explanation for this?Also when operated by division operator gives the rest of the number as the quotient
(Note only when the divisor is 10)

 

[Stephen Tashi]

(Note only when the divisor is 10)

Are you asking why k (mod 10) is equal to the integer corresponding to the last digit in the representation of k base 10 ?

 

[metapuff]

This allows you to do really fun calculations, actually. Quick, what are the last two digits of 7⁴⁸²? Well, that's just 7⁴⁸² (mod 100). Since 7 and 100 are relatively prime, and since φ(100) = 40 (where φ is the Euler phi function), 7⁴⁰ = 1 (mod 100), and so 7⁴⁸² = 7² (mod 100) = 49. So the last two digits are 49. Amaze your friends with this! ;)

 

[Rishav sapahi]

Are you asking why k (mod 10) is equal to the integer corresponding to the last digit in the representation of k base 10 ?

Yes , for me , its very much amusing .This thing is forcing me to study number theory .