From Prime Factors to Counting

Divisors from exponents: multiply (e+1) across primes for divisor count.

Try this in Python

def divisor_count(factors):
    prod = 1
    for _, e in factors:
        prod *= e + 1
    return prod

print(divisor_count([(2, 3), (3, 1)]))

Key takeaways

• Prime factorization uniqueness is the engine.
• Distinguish ordered vs unordered factorizations.
• Modulo after every multiply in contests.