Reduce the following fractions to simplest form :
`205/287`

Answer

To reduce the fraction \( \frac{205}{287} \) to its simplest form, we will follow these steps:

### Step 1: Find the Greatest Common Divisor (GCD)
First, we need to find the GCD of the numerator (205) and the denominator (287).

### Step 2: Prime Factorization
We can factor both numbers:
- For 205:
- 205 is divisible by 5 (since it ends in 5).
- \( 205 \div 5 = 41 \).
- So, \( 205 = 5 \times 41 \).

- For 287:
- 287 is divisible by 41 (since \( 287 \div 41 = 7 \)).
- So, \( 287 = 41 \times 7 \).

### Step 3: Cancel the Common Factors
Now we can rewrite the fraction using the factors we found:
\[ \frac{205}{287} = \frac{5 \times 41}{41 \times 7} \]
We can cancel out the common factor of 41:
\[ \frac{5 \times \cancel{41}}{\cancel{41} \times 7} = \frac{5}{7} \]

### Step 4: Check for Further Reduction
Now we check if \( \frac{5}{7} \) can be reduced further. The numbers 5 and 7 have no common factors other than 1.

### Final Answer
Thus, the simplest form of the fraction \( \frac{205}{287} \) is:
\[ \frac{5}{7} \]

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