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Understanding the divisibility by 5 is incredibly straightforward. A number is divisible by 5 if the last digit is either 0 or 5. This rule stems from the fact that our decimal system is based on the powers of 10, and 5 is a factor of 10. As a result, any number that ends in 0 or 5 can be evenly divided by 5.

When you encounter a problem asking whether a large number, like 704,995, is divisible by 5, all you need to do is check the last digit. In this example, the last digit is 5, which immediately tells us that it follows the rule for divisibility by 5. No need to perform any complex calculations or know the entire number — the last digit gives us a quick and conclusive answer. This simple rule can streamline your problem-solving process, saving you time and effort on tests and homework.

The last digit rule is a crucial aspect of understanding divisibility, as it provides quick shortcuts to determine if a number can be evenly divided by certain numbers such as 2, 5, or 10. For 5, as we saw previously, if the number ends in 0 or 5, it is divisible by 5. In addition to its application with divisibility by 5, this rule is used for other bases, such as divisibility by 2 (the last digit is even) or by 10 (the last digit is 0).

This rule is particularly beneficial because it requires only a glance at the unit's place of a number, making it one of the simplest divisibility tests. It also reinforces the concept of place value, emphasizing that the position of a digit within a number affects its value and properties. With the understanding of this rule, complex numbers can be dealt with ease, supporting efficient mathematical calculations without the need for extensive division.

When the last digit rule indicates divisibility but we want to find out exactly how many times the divisor fits into the dividend, we use long division. Long division is a step-by-step process of division wherein you divide, multiply, and subtract, then bring down the next digit of the dividend, repeating this sequence until you've worked through all the digits. It's the traditional method taught for dividing multi-digit numbers.

In the example of 704,995 divided by 5, performing long division would give a quotient (the answer to a division problem) of 140,999 and a remainder of 0 — confirming that 704,995 is indeed divisible by 5. Understanding long division is important because it's not only useful for testing divisibility but also for dividing any large numbers, even if the divisor is not as simple as 5. Additionally, this method reinforces other mathematical concepts such as multiplication and subtraction, making it a comprehensive tool in arithmetic.