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Modulo Arithmetic & Congruence · Question 35 of 97

Question 35

MediumOriginal question

What is the last digit of $3^{2026}$ ?

1

Correct answerYour answer

3

Correct answerYour answer

7

Correct answerYour answer

9

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Last digits of powers of 3 repeat in a cycle of 4: 3, 9, 7, 1.
$2026 \bmod 4 = 2$ , so the last digit is the second in the cycle, 9.

Worth noting

7 is the third in the cycle: $2026 = 4 \times 506 + 2$ , not $+ 3$ .

Concept: The last digit of a power
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsModular addition, subtraction and multiplication

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