lastdigitn

lastdigitn is a mathematical concept referring to the final digit of an integer when written in base ten. This digit is determined by the remainder when the integer is divided by ten. For example, the last digit of 123 is 3, because 123 divided by 10 leaves a remainder of 3. Similarly, the last digit of 50 is 0, as 50 divided by 10 has a remainder of 0. The last digit of a negative integer is also determined by this remainder, though conventions can vary. For -17, the remainder when divided by 10 is 3, making 3 the last digit.

Understanding the last digit is useful in various arithmetic operations and number theory problems. For instance, the last digit of a product of two integers is the last digit of the product of their last digits. The last digit of a power of an integer often follows a cyclical pattern. For example, powers of 2 end in the sequence 2, 4, 8, 6, 2, 4, 8, 6, and so on. This property allows for quick determination of the last digit of large powers without calculating the full value. The concept is fundamental in divisibility rules and modular arithmetic.