# Any number operated by modulus operator gives remainder as the last digit of the number?

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1. Oct 21, 2014

### 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)

2. Oct 25, 2014

### Stephen Tashi

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

3. Oct 25, 2014

### 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! ;)

4. Oct 25, 2014

### Rishav sapahi

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

Last edited: Oct 25, 2014