Question

what is the units digit in 7 hole power 213​

Answer 1

Step-by-step explanation:

7¹ = 7

7² = 49

7³ = 343

7^4 ends with 1

7^5 ends with 7

=> 212 is divisible by 4

so 1 remaining => 7^213 = 7¹ = 7

.•. 7^213 ends with 7

Answer 2

Answer:

The unit digit of $7^{213}$ is 7

Step-by-step explanation:

Required to find the unit digit in $7^{213}$

Solution:

$7^1 = 7\\7^2 = 49\\7^3 = 343\\7^4 = 2401\\7^5 = 16807$

Hence we can conclude that for n = 0,1,2,3,4,..............

$7^{4n+1}$ ends with 7

$7^{4n+2}$ ends with 9

$7^{4n+3}$ ends with 3

$7^{4n+4}$ ends with 1

Since 213 = 4×53+1, it is of the form 4n+1.

∴$7^{213}$ ends with 7

The unit digit of $7^{213}$ is 7

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