Question

What is the unit's digit of
${7}^{139}$


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Answer 1

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(7^139) = {7^(136 + 3)} = {7^(4 × 34 + 3)} = 7^(4 × 34) × 7^3

We know that cyclicity of 7 is 4 only, so (7^(4 × 34)) will have the unit digit 1

⇒ Unit digit of (7^139) = Unit digit of (1 × 7^3) = Unit digit of 343

∴ Unit digit of (7^139) = 3