- #1
Oster
- 85
- 0
1. What is the last digit of 2009^2009
I think you go about this by factoring 2009 as 7*7*41. I'm pretty much stuck.
I think you go about this by factoring 2009 as 7*7*41. I'm pretty much stuck.
micromass said:To simplify dick's post: it suffices to look at 9^1, 9^2, 9^3,..., do you see why?
The last digit of a number is determined by its remainder when divided by 10. Thus, to find the last digit of 2009^2009, we can simply calculate the remainder when 2009 is divided by 10, which is 9. As 9 raised to any power will always end in 9, the last digit of 2009^2009 is also 9.
Yes, you can use a calculator to find the last digit of 2009^2009. Simply enter 2009^2009 into the calculator and look at the last digit of the result.
Yes, there is a pattern known as the cyclicity of numbers. This pattern shows that the last digit of a number raised to successive powers will repeat in a specific pattern. For example, the last digit of 2^1 is 2, 2^2 is 4, 2^3 is 8, 2^4 is 6, and then it will repeat in this pattern. Knowing this pattern can make it easier to find the last digit of large powers.
Yes, there is a mathematical formula known as the binomial theorem that can be used to find the last digit of large powers. However, in the case of 2009^2009, the binomial theorem would not be the most efficient method as the last digit is easily determined by the remainder when divided by 10.
Finding the last digit of a number raised to a large power may be important in certain mathematical calculations or in coding and encryption. It can also be used as a problem-solving exercise to practice mathematical concepts and patterns.