  We determine the order of magnitude of H^{(k+1)}(x,\vec{y},2\vec{y}), the
number of integers up to x that are divisible by a product d_1...d_k with
y_i<d_i\le 2y_i, when the numbers \log y_1,...,\log y_k have the same order of
magnitude and k\ge 2. This generalizes a result by K. Ford when k=1. As a
corollary of these bounds, we determine the number of elements up to
multiplicative constants that appear in a (k+1)-dimensional multiplication
table as well as how many distinct sums of k+1 Farey fractions there are modulo
1.
