Find the greatest number which is such that when 76, 151, and 226 are divided by it, the remainders are all alike.
A)60
B)70
C)75
D)69

Options

A. 60
B. 70
C. 75
D. 69

Answer

To solve the problem of finding the greatest number that gives the same remainder when dividing 76, 151, and 226, we can follow these steps:

### Step 1: Calculate the differences between the numbers.
We first find the differences between the pairs of numbers:
- Difference between 151 and 76:
\[ 151 - 76 = 75 \]
- Difference between 226 and 151:
\[ 226 - 151 = 75 \]
- Difference between 226 and 76:
\[ 226 - 76 = 150 \]

### Step 2: Find the greatest common divisor (GCD) of the differences.
Now we need to find the GCD of the differences we calculated:
- The differences are 75, 75, and 150.

We can find the GCD of 75 and 150:
- The factors of 75 are: 1, 3, 5, 15, 25, 75
- The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The greatest common divisor is 75.

### Step 3: Check the options.
Now we check the options given in the question:
A) 60
B) 70
C) 75
D) 69

Since 75 is one of the options and it is the greatest number that divides the differences, we conclude that the answer is:

### Final Answer:
C) 75

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