What is the remainder when 3^35 + 6^24 is divided by 10?

For 3^35 I’m getting the Unit digit is 3 because 35 is a multiple of 5 and 3^5 is 243. Please explain what I’m doing wrong.

What is the remainder when 3^35 + 6^24 is divided by 10?

For 3^35 I’m getting the Unit digit is 3 because 35 is a multiple of 5 and 3^5 is 243. Please explain what I’m doing wrong.

3^5/10 is not unique from 3^1/10 in terms of remainders. So, you only have 4 repeating unit digits (3^1 = 3, 3^2 = 9, 3^3 = 7, 3^4 = 1). So you want to get as closed as you can to 3^35 with your highest repeating unit digit, and then count from there. I want to leave the rest to you, but feel free to ask more questions.

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I think I understand now. So i should count to find the nearby multiples. 34 is a multiple of 2 and 36 is a multiple of 4. So the 35 would be in between those two making 7 the unit digit.

That is not necessarily how I though about it, and I’m not sure if that works in every case but I think it does? How I think about it is basically you get to the closest number, in our case 32 because 32 is a multiple of 4, and then count the repeats until you get to 35, so first go to 3^1 (33) then 3^2 (34), and finally 3^3(35).