THE VALUE 2 TO THE 8TH POWER - 1 IS DIVISIBLE BY THREE PRIME NUMBERS. WHAT IS THE SUM OF THE THREE PRIME NUMBERS?
Just start at 2 and divide 255 which is (2^8)-1.
255/2 =127.5
Not divisible by 2.
255/3 = 85
We have one prime number, 3.
255/5 = 51
We have two prime numbers - 3,5.
255/7 = 36.43
Not divisible by 7
255/9 = 28.33
Not divisible by 9
255/11 = 23.18
Not divisible by 11
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255/17 = 15
We have three prime numbers - 3,5,17.
So the sum of them are:
3+5+17 = 25
or, since a^2-b^2 = (a-b)(a+b)
(2^8-1) = (16-1)(16+1) = (4-1)(4+1)(16+1) = 3*5*17
To find the sum of the three prime numbers that divide the value 2 to the 8th power minus 1, we first need to calculate the value.
2^8 - 1 can be simplified as follows:
2^8 = 256
256 - 1 = 255
Now, let's find the prime factors of 255.
The prime factors of 255 are 3, 5, and 17.
Therefore, the sum of the three prime numbers is:
3 + 5 + 17 = 25
To find out if the value 2 to the 8th power minus 1 is divisible by three prime numbers, we first need to calculate this value.
2 to the 8th power means multiplying 2 eight times: 2^8 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 256.
Next, we subtract 1 from this value: 256 - 1 = 255.
Now, let's check if 255 is divisible by any prime numbers. We'll divide it by prime numbers starting from 2 and increasing until we find three prime numbers that divide it.
255 divided by 2 gives us a remainder of 1. So it is not divisible by 2.
255 divided by 3 gives us a quotient of 85 with no remainder. So it is divisible by 3.
Thus, we have found one prime number that divides 255: 3. But we need to find two more prime numbers.
255 divided by 5 gives us a remainder of 0. So it is divisible by 5.
Therefore, we have found another prime number that divides 255: 5. Now we need to find the final one.
255 divided by 7 gives us a remainder of 6. So it is not divisible by 7.
Finally, we have found three prime numbers that divide the result 2^8 - 1 (which is 255): 3, 5, and 7.
To find the sum of these three prime numbers, we add them together: 3 + 5 + 7 = 15.
Therefore, the sum of the three prime numbers that 2 to the 8th power minus 1 is divisible by is 15.