document.write( "Question 1150795: What is the last digit of 7^72 ? Thanks! \n" ); document.write( "
Algebra.Com's Answer #772251 by greenestamps(13206)\"\" \"About 
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\n" ); document.write( "Look at the pattern in the final digits of 7^n for increasing powers n. Since we are only interested in the final digit, we only need to keep the last digit after each multiplication.
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document.write( "  7^1 final digit 7\r\n" );
document.write( "  7^2 final digit 9  (7*7 = 49)\r\n" );
document.write( "  7^3 final digit 3  (9*7 = 63)\r\n" );
document.write( "  7^4 final digit 1  (3*7 = 21)\r\n" );
document.write( "  7^5 final digit 7  (1*7 = 7)\r\n" );
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\n" ); document.write( "It should be clear that the sequence of final digits repeats ever 4 powers.

\n" ); document.write( "Since the power 72 is a multiple of 4, the final digit of 7^72 is the same as the final digit of 7^4, which is 1.

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