Three schools decide to collect money among their students to donate to various charitable institutions. If the first one collects 120 thousand, the second 280 thousand and the third 360 thousand pesos, what is the largest amount that each institution will receive so that it is the same and how many institutions can benefit?

### 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.