Contents
What is the last digit of 2 5014?
Powers of 2 (starting from 2^1) are 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, … We can notice that the last digits are 2, 4, 8, 6, 2, 4, 8, 6, 2, 4, 8, …
How do you find what power of 2 A number is?
Explanation. A simple method for this is to simply take the log of the number on base 2 and if you get an integer then the number is the power of 2.
What are the last two digits of 7 to the power 2008?
Find the last two digits of 72008 (CAT 2008) So, the last two digits are 01.
What is the last digit of 5 power 2020?
Answer: the last digit of 5 to the power of 2020 is 25 because 5^6=78125 you will observe that any number will have 25 as the last two digits. And the pattern will repeat till 5^100.
What is the last digit of 7 power 100?
so the last digit of 7100 is 1.
What is the last digit of 7 355?
Fermat: Last two digits of 7355 Since the answer is 7355≡3(mod5), the last digit is either 3 or 8. Since 7 is odd, the answer will clearly be odd, so 3 is it.
What is 2 the power of 3?
Answer: 2 raised to the third power is equal to 23 = 8. Explanation: 2 to the 3rd power can be written as 23 = 2 × 2 × 2, as 2 is multiplied by itself 3 times. Here, 2 is called the “base” and 3 is called the “exponent” or “power.”
How to find the last digits of a large power?
A common exercise in number theory is to find the last digits of a large power, like 2 2009, without using a computer. 2 2009 is a 605-digit number, so evaluating it by hand is out of the question. So how do you find its last digits — efficiently?
Is there a power of two that ends in 02?
Although there is no power of two that ends in 02, we can use any two-digit ending that is a power of two; we just convert it to 2 y using the laws of exponents. Let’s go back to our example, 2 2009.
Which is the last digit of 2 N?
The last m digits of 2 n are the digits in the table with the label corresponding to that remainder. For example, let’s find the last digit of 2 2009. The last digit of the positive powers of two cycles with length 4, and . According to the table, a remainder of 1 corresponds to a last digit of 2.
How to print the last k digits of a ^ B?
First Calculate a^b, then take last k digits by taking modulo with 10^k. Above solution fails when a^b is too large, as we can hold at most 2^64 -1 in C/C++. The efficient way is to keep only k digits after every multiplication.