whats the last two digits of 5 to the 347 power
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To find the last two digits of 5 raised to the power of 347, we need to determine the pattern of the last two digits of powers of 5.
Let's start by listing the last two digits of the powers of 5:
5^1 = 05
5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3125
5^6 = 15625
5^7 = 78125
...
and so on.
From observing the pattern, we can see that the last two digits repeat every four powers. Therefore, to find the last two digits of 5^347, we divide 347 by 4 to determine the remainder.
347 divided by 4 gives a remainder of 3.
Now, we look at the list of last two digits again and find the power that corresponds to a remainder of 3, which is 5^3 = 125.
Thus, the last two digits of 5^347 is 125.
To find the last two digits of 5 to the power of 347, we can use the concept of modular arithmetic.
Step 1: Find the remainder when 347 is divided by 4.
347 divided by 4 gives a remainder of 3.
Step 2: Find the powers of 5 modulo 100.
The powers of 5 modulo 100 repeat in a cycle of 20: 5, 25, 25, 25, ...
Step 3: Determine the power of 5 modulo 100 based on the remainder obtained in step 1.
Since the remainder is 3, the power of 5 modulo 100 will be the third term in the cycle, which is 25.
Therefore, the last two digits of 5 to the power of 347 is 25.