06-09-2017, 05:19 PM
(This post was last modified: 06-09-2017, 05:19 PM by Dane Regan.)
Voted
The last digit of 3^2198634
Answer:[spoiler]
9
The last digit of the following are:
3^1: 3
3^2: 9
3^3: 7
3^4: 1
3^5: 3
etc. The pattern repeats as the last digit of two numbers being multiplied are the only digits that affect the last digit of the product. Therefore, the last digit of 3^(4n+2) where n is an integer (i.e. a multiple of 4 plus 2) is 9. To tell that 2198634 is a multiple of 4 + 2, look at the last 2 digits: 34. 34 = 32 + 2 = 4*8 + 2. This method works as 4 is a factor of 100.[/spoiler]
The last digit of 3^2198634
Answer:[spoiler]
9
The last digit of the following are:
3^1: 3
3^2: 9
3^3: 7
3^4: 1
3^5: 3
etc. The pattern repeats as the last digit of two numbers being multiplied are the only digits that affect the last digit of the product. Therefore, the last digit of 3^(4n+2) where n is an integer (i.e. a multiple of 4 plus 2) is 9. To tell that 2198634 is a multiple of 4 + 2, look at the last 2 digits: 34. 34 = 32 + 2 = 4*8 + 2. This method works as 4 is a factor of 100.[/spoiler]