To express the number 12523 as a product of identical factors, we will first need to check if it can be factored into smaller components.
After analyzing, we find that:
\[ 12523 = 125 \times 100 + 23 \] This does not help in simplification.
If we try to factor 12523, we notice that it is not a perfect square and might not have simple factors. After some calculations, we find that 12523 is actually a prime number.
As it stands, 12523 cannot be factored into simpler products of identical factors other than 1 and itself. Therefore, in its simplest form, it stays as:
12523
If you meant to ask for prime factorization instead or had a different number in mind, please let me know!