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MICRO LESSON / 01Units digit.
Units digit.
Big powers.
Small patterns.
Why do powers of 7 end in the same four digits, again and again?
NUMBER SYSTEMS
Look at the repeating pattern.
Only the last digit matters. Repeatedly multiplying by 7 gives these units digits:
7¹7
7²9
7³3
7⁴1
The pattern then repeats: 7, 9, 3, 1. To find the units digit of 72026, divide the exponent by 4. Remainder 2 means the second digit in the cycle: 9.
REMEMBERWhen a power cycle has length 4, remainder 0 means choose the 4th digit—not the first.
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Original practice • Not official PYQs