+9673 What is the last digit of 7^399 :O
Saw this on one Maths Olympiad paper(That's a kind of mathematic competition)
+118670 Hi Max
What is the last digit of 7^399
7^1 ends in 7
7^2 ends in 9
7^3 ends in the last digit of 9*7 which is 3
7^4 ends in the last digit of 3*7 which is 1
7^5 ends in the last digit of 1*7 which is 7
so now we have the pattern.
7,9,3,1,7,9,3, etc
there are four numbers in the pattern
7^(4n+1)=7
7^(4n+2)=9
7^(4n+3)=3
7^(4n) = 1
where n is a integer greater or equal to 0.
399 = 400-1 = -1 mod 4 which is the same as 3 mod 4
or if you would rather
399= 4*99+3 see the remainder is 3 so 399=3 mod4
7^(399) = 7^(99*4+3) So the last digit will be 3
+118670 Hi Max
What is the last digit of 7^399
7^1 ends in 7
7^2 ends in 9
7^3 ends in the last digit of 9*7 which is 3
7^4 ends in the last digit of 3*7 which is 1
7^5 ends in the last digit of 1*7 which is 7
so now we have the pattern.
7,9,3,1,7,9,3, etc
there are four numbers in the pattern
7^(4n+1)=7
7^(4n+2)=9
7^(4n+3)=3
7^(4n) = 1
where n is a integer greater or equal to 0.
399 = 400-1 = -1 mod 4 which is the same as 3 mod 4
or if you would rather
399= 4*99+3 see the remainder is 3 so 399=3 mod4
7^(399) = 7^(99*4+3) So the last digit will be 3
