unit digit in 122^122 × 133^133
Answers
1.01898453E537
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Unit digit of 122¹²² × 133¹³³ is 2
Explanation:
Given:
122¹²² × 133¹³³
To find:
The unit digit of 122¹²² × 133¹³³
We know that,
==> Cyclicity of 1 is 1
==> Cyclicity of 2 is 4
==> Cyclicity of 3 is 4
==> Cyclicity of 4 is 2
==> Cyclicity of 5 is 1
==> Cyclicity of 6 is 1
==> Cyclicity of 7 is 4
==> Cyclicity of 8 is 4
==> Cyclicity of 9 is 2
==> Cyclicity of 10 is 1
Step1: Find the unit digit of 122¹²²
==> The last digit of 122 is 2
==> l=2
==> Cyclicity of 2 is 4
==> Then the power is divided by 4
==> 122÷4
==> The remainder is 2
==> let remainder is x
==> x=2
==> Unit digit is lˣ
==> unit digit of 122¹²² is 2²
==> unit digit of 122¹²² is 4
Step2: Find the unit digit of 133¹³³
==> The last digit of 133 is 3
==> l=3
==> Cyclicity of 3 is 4
==> Then the power is divided by 4
==> 133÷4
==> The remainder is 1
==> let remainder is x
==> x=1
==> Unit digit is lˣ
==> Unit digit of 133¹³³ is 3¹
==> Unit digit of 133¹³³ is 3
Step3: Find the unit digit of 122¹²² × 133¹³³
==> Unit digit of 122¹²² is 4
==> Unit digit of 133¹³³ is 3
==> Unit digit of 122¹²² × 133¹³³ = 4 × 3
==> Unit digit of 122¹²² × 133¹³³ = 12
==> Unit digit of 122¹²² × 133¹³³ is 2