Find the largest number that divides 76, 115 and 154 leaving remainder 11 in each case

Answer

To find the largest number that divides 76, 115, and 154 leaving a remainder of 11 in each case, we can follow these steps:

### Step 1: Subtract the remainder from each number
To eliminate the remainder, we subtract 11 from each of the numbers:

- For 76:
\( 76 - 11 = 65 \)

- For 115:
\( 115 - 11 = 104 \)

- For 154:
\( 154 - 11 = 143 \)

### Step 2: List the numbers obtained
After subtracting 11 from each number, we have:
- 65
- 104
- 143

### Step 3: Find the factors of each number
Now, we will find the factors of each of these numbers:

- Factors of 65:
\( 1, 5, 13, 65 \)

- Factors of 104:
\( 1, 2, 4, 8, 13, 26, 52, 104 \)

- Factors of 143:
\( 1, 11, 13, 143 \)

### Step 4: Identify the common factors
Now, we will identify the common factors among 65, 104, and 143. The common factors are:
- 1
- 13

### Step 5: Find the highest common factor (HCF)
The highest common factor among the common factors is:
- **13**

### Conclusion
Thus, the largest number that divides 76, 115, and 154 leaving a remainder of 11 in each case is **13**.

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