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Chapter 2: Problem 33

Determine whether 256 is divisible by 16 .

Short Answer

Expert verified
Yes, 256 is divisible by 16.

Step by step solution

01

Understand Divisibility

To determine if a number is divisible by another, the result of the division must be an integer without any remainder. In mathematical terms, if a number is divisible by another, there exists an integer such that the division result is exactly that integer.
02

Perform the Division

Divide 256 by 16 and determine if the result is an integer. Using the division formula, \(\frac{256}{16} = 16\)
03

Check for Remainder

After performing the division, check if there is any remainder. In this case, \(\frac{256}{16} = 16\) is an exact division with no remainder.
04

Conclusion

Since the result of the division is an integer without any remainder, 256 is divisible by 16.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integer Division
Integer division is a fundamental concept in arithmetic. It refers to dividing one whole number by another, resulting in another whole number. Think of it as dividing a set of items into equal groups.
For example, if you have 16 apples and you want to distribute them evenly among 4 friends, each friend would get 4 apples.
Division is only considered integer division when the result of the calculation is a whole number without any fractional or decimal parts.
No Remainder
When we perform division and the result is a whole number, we say there's 'no remainder'.
In our example of dividing 256 by 16, the quotient is exactly 16. There are no extra parts left over after the division.
Using simple arithmetic, if you try to break something into equal parts and nothing is left over, you have no remainder. This is a clear indicator of divisibility.
For instance, if 20 candies are divided evenly among 4 children, each child gets 5 candies and none are left, showing no remainder.
Basic Arithmetic
Basic arithmetic covers fundamental math operations like addition, subtraction, multiplication, and division.
Understanding these operations is essential for more complex math later on.
In our exercise, we applied division, which is just splitting a number into equal parts.
  • First, 256 (the total) is divided by 16 (the divisor).
  • The result here is 16, a whole number.
  • Since there's no remainder, the division confirms basic arithmetic principles of equal splitting.
This simplicity helps lay the groundwork for more advanced concepts encountered in higher math studies.

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Most popular questions from this chapter

Find the prime factorization of each number. $$ 25 $$

Find another name for the given number, but with the denominator indicated. Use multiplying by 1 . $$ \frac{5}{12}=\frac{?}{48} $$

Multiply by \(1,2,3,\) and so on, to find ten multiples of each number. $$ 50 $$

The pitch of a screw is the distance between its threads. With each complete rotation, the screw goes in or out a distance equal to its pitch. Use this information. The pitch of a screw is \(\frac{3}{32}\) in. How far will it come out of a piece of plywood when it is turned 10 complete rotations counterclockwise?

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