Divisibility Rules - 4, 5, 8, 10 – Practice Problems

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Have you ever wondered why some numbers will divide evenly (without a remainder) into another number, while others will not? Divisibility rules help us determine if a number will divide into another number without actually having to divide. This video shows examples of the divisibility rules for 4, 5, 8, and 10.

The divisibility rules for 4, 5, 8, and 10 are as follows:

The Rule for 4: a number is divisible by 4 if its last two digits are evenly divisible by 4. For example, 2312. The last two digits are 12 and it is divisible by 4. Thus, 2312 is divisible by 4.
The Rule for 5: a number is divisible by 5 if it ends with 0 or 5. For example, 3750 and 42755. The two numbers end with 0 and 5. Thus, these numbers are divisible by 5.
The Rule for 8: a number is divisible by 8 if the last three digits are evenly divisible by 8. For example, 17216. The last three digits are 216 and it is divisible by 8. Thus, 17216 is divisible by 8.
The Rule for 10: a number is divisible by 10 if it ends with 0. For example, 35070. The number ends with 0, therefore the number is divisible by 10.

Note that once a number doesn’t satisfy a rule, then that number is not divisible by the number that rule is for. There is a divisibility rule for every number. However, some of the rules are easier to use than others. For the rest, it might be simpler to actually divide.

Compute fluently with multi-digit numbers and find common factors and multiples.


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Exercises in this Practice Problem
Decide which number is divisible by $4$.
Find the correct statements for divisibility rules for 4, 5, 8, and 10.
Explain why the numbers are divisible using the rules for divisibility.
Determine if the numbers are divisible by $4$ or $5$.
Calculate in which cases numbers are divisible by $2$.
Find the numbers that are divisible by $8$.