### Step 1: Determine the GCD of the amounts collected
The amounts collected are:
- 120,000 pesos
- 280,000 pesos
- 360,000 pesos
Let's calculate the GCD of these three numbers.
### Step 2: Calculate the GCD
First, let's factor each number:
- 120,000 = 2^6 \times 3 \times 5^4
- 280,000 = 2^4 \times 5^4 \times 7
- 360,000 = 2^4 \times 3^2 \times 5^4
The GCD is the product of the lowest powers of all the common prime factors:
- The common prime factors are 2^4 and 5^4.
Thus, the GCD is:
GCD = 2^4 \times 5^4 = 16 \times 625 = 10,000
### Step 3: Determine the number of institutions that can benefit
Now, divide the total amount collected by the GCD:
- Total amount collected = 120,000 + 280,000 + 360,000 = 760,000 pesos.
- Number of institutions = \frac{760,000}{10,000} = 76 .
### Final Answer:
- The largest amount each institution will receive is **10,000** pesos.
- **76** institutions can benefit from the donation.