7^202

[jverga]

Does anyone remember how to solve for the 'units' digit here? I know there's the grid:

0 - 0000000...
1 - 111111....
2 - 24862...
3 - 3971....

how do i do it for 7^202? thanks

[garima_aries01]

for 7 the sequence is

7,9,3,1,7

So the sequence repeats after 4 multiplications.
=>
If the remainder is 1 on division of power by 4 : units place will be 7
If the remainder is 2 on division of power by 4 : units place will be 9
If the remainder is 3 on division of power by 4 : units place will be 3
If the remainder is 0 on division of power by 4 : units place will be 1

for 7^202 :

divide 202 by 4 we get remainder 2
so the unit place will be 9

[RonPurewal]

for 7 the sequence is

7,9,3,1,7

So the sequence repeats after 4 multiplications.
=>
If the remainder is 1 on division of power by 4 : units place will be 7
If the remainder is 2 on division of power by 4 : units place will be 9
If the remainder is 3 on division of power by 4 : units place will be 3
If the remainder is 0 on division of power by 4 : units place will be 1

for 7^202 :

divide 202 by 4 we get remainder 2
so the unit place will be 9

excellent.