What least number must be added to 754 so that the sum is completely divisible by 59?

Options

A. 21
B. 13
C. 16
D. 7

Answer

To solve the problem of finding the least number that must be added to 754 so that the sum is completely divisible by 59, we can follow these steps:

### Step 1: Divide 754 by 59
First, we need to find out how many times 59 fits into 754. We perform the division:

\[ 754 \div 59 \approx 12.76 \]

This means 59 fits into 754 approximately 12 times.

### Step 2: Multiply the quotient by 59
Next, we multiply the integer part of the quotient (which is 12) by 59 to find the largest multiple of 59 that is less than or equal to 754:

\[ 12 \times 59 = 708 \]

### Step 3: Calculate the remainder
Now, we need to find the remainder when 754 is divided by 59:

\[ 754 - 708 = 46 \]

So, the remainder is 46.

### Step 4: Find the difference from 59
To make 754 completely divisible by 59, we need to find out how much more we need to add to 754 to reach the next multiple of 59. We do this by subtracting the remainder from 59:

\[ 59 - 46 = 13 \]

### Conclusion
Thus, the least number that must be added to 754 to make it completely divisible by 59 is:

\[ \text{Answer} = 13 \]