Expressing an even number in powers of 2 and a multiple of an odd number.

for example, i have a number 52.

52= (2^2)*13. where 13 is odd and 4 is the power of 2. i mean, i want to express a number a=(2^r)*d, where d is odd. as soon as, for any number d becomes odd i want to stop it factorisding.

for 52 here,

52=(2^1)*26

here 26 is even.

so again, 52=(2^2)*13. i want matlab to give me this expression for any even number.

Another example is, 80=(2^1)*40, next 80=(2^2)*20, again, 80=(2^3)*10, again 80=(2^4)*5. in here d=5, which is odd. this is the expression i want for 80.

I don't need to see the whole steps as its calculating the powers of 2. i just want it to give me the last expression.

Does anyone have an idea how to do it?

Answer 1

[Guillaume]

Can't you just use a loop?

function [exponent, multiplicand] = decompose(number)
    validateattributes(number, {'numeric'}, {'integer', 'positive', 'even'});
    for exponent = 1:1024  %no point going any higher. maximum exponent of a double is 1023
        multiplicand = number / 2^exponent;
        if mod(multiplicand, 2) == 1  %multiplicand is odd
            break;
        end
    end
    assert(exponent ~= 1024, 'no odd multiplicand found');
end

And actually, since there's only 1023 valid exponents, you could do it without a loop:

function [exponent, multiplicand] = decompose(number)
    validateattributes(number, {'numeric'}, {'integer', 'positive', 'even'});
    exponents = 1:1023;
    multiplicands = number ./ 2.^exponents;
    firstodd = find(mod(multiplicands, 2) == 1, 1);
    exponent = exponents(firstodd);
    multiplicand = multiplicands(firstodd);
end

Answer 2

[M]

I would do something like

a = 80;
r = 1;
d = a/2;

while mod(d,2)==0
    r=r+1;
    d=d/2;
end

[rihan jericho]

i also want it to give me the numbers stored, for example after the loop is done i want it to give me r=4, d=5 for 80. as 80 = (2^4)*5.

i also want to do it generally for which i casn use input. but this is the ultimate expression for any even number input i want.