Problem 42510. Divisible by n, Composite Divisors

Pursuant to Divisible by n, prime vs. composite divisors, this problem requires you to write a function that determines divisibility for a large number (n_str) when the divisor is a composite. As was required in that problem, you will need to formulate the highest-power factorization of the divisor. Divisibility of n_str can then be determined by testing against each highest-power factor. For simplicity, this problem is restricted to numbers that contain the following as highest-power factors: 2, 3, 4, 5, 8, 9, and 10, as these divisibility tests are trivial. Their rules are included briefly below, for reference.

As an example, a number is divisible by 30 if it is divisible by 2, 3, and 5, as those are the highest-power factors for 30. Likewise, a number is divisible by 36 if it is divisible by 4 and 9 (not 3), as those are its highest-power factors.

The only restriction that remains is Java.

• Divisible by 2: if the last digit is divisible by 2.
• Divisible by 3: if the sum of the number's digits (n_str) is divisible by 3. Apply iteratively, as necessary, to arrive at a single-digit number.
• Divisible by 4: if the last two digits are divisible by 4.
• Divisible by 5: if the last digit is a 0 or 5.
• Divisible by 8: if the last three digits are divisible by 8.
• Divisible by 9: if the sum of the number's digits (n_str) is divisible by 9. Apply iteratively, as necessary, to arrive at a single-digit number.
• Divisible by 10: if the last digit is zero.

Previous problem: Divisible by n, Truncated-number Divisors.