Posted by **Anonymous** on Friday, August 3, 2012 at 10:01pm.

What are the final two digits of 7^177

- math -
**Count Iblis**, Friday, August 3, 2012 at 11:35pm
Phi(100) = 40, so the order of 7 (i.e. the smallest power to which you have to raise 7 to get 1) is a divisor of 40, and you easily find that it is 4.

Computing Mod 100 in the following:

7^4 = 2401 = 1

176 is a multiple of 4, so we have:

7^177 = 7

- math -
**Reiny**, Friday, August 3, 2012 at 11:37pm
Hint: take a look at the last two digits for the first few powers of 7

7^1 = 7 or 07

7^2 = 49

7^3 = 343

7^4 = 2401

7^5 = 16807

7^6 = ......49

7^7 = ......43

7^8 = ......01

7^9 = ......07

7^10 = .... 49

I am sure you can do something with this pattern.

## Answer This Question

## Related Questions

- al gebr word problem MATH - parts to fix your car cost $55.35. the mechanic ...
- math - 1. a door code is made up of six unique digits the last digit is 8. 2....
- math - Solve the mathematical puzzle. Determine the digits of F from these clues...
- MATH - What is my number if the hundreds digit is less than the tens digit and ...
- math (5th grade) - There are two 1's, two 2's, and two 3's. There is one digit ...
- math - A locker combination has three nonzero digits, and digits cannot be ...
- math - A locker combination has three nonzero digits, and digits cannot be ...
- Math - A locker combination has three nonzero digits, and digits cannot be ...
- math - What are the final two digits of 7124? Show work to support your answer
- Math - A locker combination has three nonzero digits, and digits cannot be ...

More Related Questions