Modulus & Division: Last Digit of Numbers Explained

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Discussion Overview

The discussion revolves around the properties of modulus and division, particularly focusing on how the last digit of numbers can be determined using the modulus operation with a divisor of 10. Participants explore the implications of this concept in number theory and its applications in calculations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants find it amusing that the modulus operation with 10 yields the last digit of a number in base 10.
  • There is a question raised about the relationship between k (mod 10) and the last digit of k, indicating a conceptual exploration of this property.
  • One participant describes a method for calculating the last two digits of a number using modulus with 100, referencing the Euler phi function and properties of relatively prime numbers.
  • Another participant expresses that this exploration into modulus is motivating them to study number theory further.

Areas of Agreement / Disagreement

Participants generally agree on the interesting nature of the modulus operation with respect to the last digit of numbers, but there is no consensus on deeper implications or applications beyond the initial observations.

Contextual Notes

The discussion does not resolve the underlying mathematical principles or assumptions related to the properties of modulus and division, nor does it clarify the implications of the Euler phi function in this context.

Rishav sapahi
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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)
 
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Rishav sapahi said:
(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 ?
 
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! ;)
 
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Stephen Tashi said:
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 .
 
Last edited:

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