$2025 = 3^4 \times 5^2$
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- \boxed{32\sqrt{3}}Question: What is the largest possible number of identical research grants that can be awarded using 2025 and 1515 units of funding, ensuring no funds remain unallocated?
- Solution: To determine the largest number of identical grants, compute $\gcd(2025, 1515)$.
- Factorize:
- $1515 = 3 \times 5 \times 101$
- The $\gcd$ is the product of the smallest powers of common primes: $3^1 \times 5^1 = 15$.
- Thus, the maximum number of grants is $\boxed{15}$.
