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 .

 

[blue_raver22]

I find this topic interesting and definitely amusing. The explanation for the last digit of numbers is related to the concept of modulus, which is a mathematical operation that calculates the remainder after division. When we divide a number by 10, the remainder will always be the last digit of the original number. This is because the decimal system is based on powers of 10, so when we divide by 10, we are essentially removing the last digit and the remainder is what is left.

Furthermore, the division operator also plays a role in this concept. When we divide a number by 10, the result is the quotient, which is the whole number part of the division. This means that the remainder, or last digit, is essentially the difference between the original number and the quotient. This is why the division operator gives the remainder as the quotient when the divisor is 10.

Overall, this phenomenon can be explained by the fundamental principles of mathematics and the decimal system. It is a fascinating concept and shows the interconnectedness of different mathematical operations.