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Integers are a set of numbers that include all positive and negative whole numbers, as well as zero. This means integers do not include fractions, decimals, or any part of a number that isn't whole. In simpler terms, if you can count it with your fingers (either forwards or backwards) and include zero, you're dealing with integers. For example:

• Positive integers: 1, 2, 3, 4, ...
• Negative integers: -1, -2, -3, -4, ...
• Zero, which is neither positive nor negative

In the context of division, when you divide two integers, the result is another integer only when the division is exact, that means it leaves no remainder.

The remainder is what is left over after dividing one integer by another. When you attempt to divide two integers and the division isn't exact, the leftover amount is called the remainder. For instance, consider dividing 10 by 3:

• 10 divided by 3 equals 3 with a remainder of 1

This means you can multiply 3 by 3 to get 9, and add the remainder of 1 to reach the original number 10. If there is no remainder, the division results in an exact whole number, or an integer. In our exercise, dividing 54 by 9 results in 6, with no remainder left over. This indicates that 9 fits perfectly into 54 and divides it evenly.

Division step-by-step involves a straightforward process to determine how many times one number can be contained within another number. Let's go through the steps for dividing two numbers in a simple, methodical way: 1. **Check the Dividend and Divisor**: Identify the numbers you are working with. The dividend is the number you are dividing, while the divisor is the number you are dividing by. In our case, 54 is the dividend and 9 is the divisor.
2. **Perform the Division**: Divide the dividend by the divisor. Calculate how many times the divisor can fit into the dividend. For our problem, divide 54 by 9, which equals 6.
3. **Determine the Quotient**: The result of your division is called the quotient. Here, the quotient is 6, meaning 9 goes into 54 six times.
4. **Check for Remainder**: After division, see if there is a remainder. If the quotient exactly divides the dividend with no number leftover, the remainder is zero as in 54 divided by 9.
This step-by-step method ensures clarity in understanding how much one integer can fully be divided by another, helping identify when a particular number is a factor of another.