The second one and the last one
There may be more brilliant solution than the following, but here are my thoughts.
We make use of Euclid's algorithm to help us out.
Consider finding the hcf of A=2^(n+x)-1 and B=2^(n)-1.
If we repeated subtract B from A until the difference C is less than B (smaller number), the hcf between A and B is the same as the hcf between B and C.
For example, we would subtract 2^x times B from A, or
C=A-2^xB=2^(n+x)-2^x(2^n-1)=2^(n+x)-2^(n+x)+2^n-1=2^n-1
By the Euclidean algorithm,
hcf(A,B)=hcf(B,C)=hcf(2^n-1,2^x-1)
If n is a multiple of x, then by repetition, we will end up with
hcf(A,B)=hcf(2^x-1,2^x-1)=2^x-1
For the given example, n=100, x=20, so
HCF(2^120-1, 2^100-1)=2^(120-100)-1=2^20-1=1048575
(since n=6x, a multiple of x).
Answer:
1,2,3,6
Step-by-step explanation:
6x1, 2x3, 3x2, 6x1
Answer:
the answer should be D
Step-by-step explanation:
:)
Answer:
the percentage increase is 360%
Step-by-step explanation:
The computation of the increase in percentage is shown below;
Given that
SOcial security credit as on 1978 is $250
And, the social security tax as on 2008 is $1,150
Now based on the above information
The percentage increase is
= ($1,150 - $250) ÷ ($250)
= 360%
Hence, the percentage increase is 360%