Why is scalar division slower than piece-wise matrix division?

Hello,

today I explained to my student that piece-wise division is much faster than a corresponding operation realized through a loop. However, I had no idea how much. Obviously it depends on the size of the matix. I, therefore, wrote follwowing exemplary code:

lengths = round(logspace(0,7));
t1s = zeros(numel(lengths),1);
t2s = zeros(numel(lengths),1);
for j=1:numel(lengths)
    tic %version a - piece-wise division
    a = ones(lengths(j),3)./(2*ones(lengths(j),1));
    t1s(j) = toc;

    tic %version b - loop
    a = ones(lengths(j),3);
    for i=1:size(a,1)
        a(i,:) = a(i,:) / 2;
    end
    t2s(j) = toc;
end

figure
hold on
ylabel('calc. time / sec');
xlabel('matrix length / -');
plot(lengths,t1s);
plot(lengths,t2s);
set(gca, 'XScale', 'log')
set(gca, 'YScale', 'log')
yyaxis right
set(gca, 'YScale', 'log')
plot(lengths,abs(t1s-t2s));
legend('Piece-wise','loop','delta');

The code divides increasing numbers of vectors by two. The result looks like this:

It comes as no surprise that piece-wise divsion is much faster than a for loop (Roughly factor 100).

But can somone please explain why both versions are relativley slow at 1<L<10?

Simon