To express the number 12523 as a product of identical factors, we can factor it into its prime factors:
First, we can check if 12523 can be factored:
- It’s not divisible by 2 (not even).
- Sum of digits (1 + 2 + 5 + 2 + 3 = 13) is not divisible by 3, so it's not divisible by 3.
- It does not end in 0 or 5, so it’s not divisible by 5.
- Continuing to test prime numbers up to the square root of 12523, we find:
After testing a few primes, we find:
12523 = 17 × 737.
7 and 37 are primes, meanwhile, 737 can be factored further:
737 = 11 × 67.
Thus, 12523 = 17 × 11 × 67.
To express this as a product of identical factors, we consider combinations. However, 12523 does not seem to have identical factors.
Since 12523 can be factorized into primes as \( 17^1 \times 11^1 \times 67^1 \), it does not simplify further into a product of identical factors like squares or cubes.
In conclusion, 12523 is already in its simplest factorization form as a product of distinct primes: 17, 11, and 67.