SOLUTION: What is the last digit of 7^72 ? Thanks!

Question 1150795: What is the last digit of 7^72 ? Thanks!
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.

Last digits of form the sequence n 1 2 3 4 5 . . . last digits of 7 9 3 1 7 . . . This sequence is periodic with the period length of 4. How many periods of the length 4 are in the sequence 1, 2, 3, 4, . . . , 72 ? The number of periods is exactly = 18, so the last digit of the number is 1. ANSWER. has the last digit 1.

Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

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.
7^1 final digit 7 7^2 final digit 9 (7*7 = 49) 7^3 final digit 3 (9*7 = 63) 7^4 final digit 1 (3*7 = 21) 7^5 final digit 7 (1*7 = 7) ...

It should be clear that the sequence of final digits repeats ever 4 powers.

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.

RELATED QUESTIONS
What is the last digit of the number 77^77... (answered by Alan3354)
what is the last non zero digit of 96!... (answered by MathLover1)
what is the last non zero digit of... (answered by edjones)
What is the last digit of 2^2008... (answered by College Student)
what is the last digit of... (answered by haileytucki)
What is the last digit of 7^2009 ? A. 1 B. 3 C. 5 D. 7 E. 9 (answered by Edwin McCravy)
What is the last digit of 93^36? a)3 b) 9 c) 7 d) 1 e) 4 (answered by Alan3354)
the sum of the last two digits of a three digit counting number is 7. the sum of the... (answered by solver91311,oscargut)
What is the largest four-digit number such that the second digit is one-fourth of the... (answered by RAY100)