Divisibility Rules

Definition

Divisibility rules are a set of guidelines that help determine whether a given whole number is divisible by another whole number without leaving a remainder. These rules are particularly useful in the context of dividing whole numbers, finding multiples and factors, and performing arithmetic operations with fractions.

5 Must Know Facts For Your Next Test

1. Divisibility rules provide a quick and efficient way to determine if a number is divisible by a specific divisor, without having to perform the actual division.
2. Knowing the divisibility rules can simplify the process of finding multiples and factors of a number, as well as adding and subtracting fractions with different denominators.
3. The divisibility rules for the numbers 2, 3, 4, 5, 6, 8, 9, and 10 are commonly used in mathematical operations.
4. Divisibility by 2 can be determined by checking if the last digit of the number is even, while divisibility by 3 can be determined by adding the digits and checking if the sum is divisible by 3.
5. Divisibility by 4 can be determined by checking if the last two digits of the number are divisible by 4, and divisibility by 8 can be determined by checking if the last three digits are divisible by 8.

Review Questions

• Explain how the divisibility rules can be used to simplify the process of dividing whole numbers.
  • The divisibility rules provide a way to quickly determine if a number is divisible by another without having to perform the actual division. For example, if you need to divide a number by 2, you can simply check if the last digit of the number is even, rather than dividing the entire number. This can save time and effort, especially when dealing with larger numbers. Additionally, the divisibility rules can help identify factors of a number, which is useful when working with fractions and finding common denominators.
• Describe how the divisibility rules can be applied to the process of finding multiples and factors of a number.
  • The divisibility rules can be used to efficiently identify the multiples and factors of a number. For instance, to find all the factors of a number, you can start by checking if it is divisible by 2, 3, 4, 5, and so on, using the divisibility rules. This allows you to quickly eliminate numbers that are not factors, rather than having to divide the number by every possible divisor. Similarly, when finding multiples of a number, you can use the divisibility rules to generate a list of potential multiples, rather than having to multiply the number by every possible factor.
• Analyze how the divisibility rules can be applied to the process of adding and subtracting fractions with different denominators.
  • The divisibility rules can be used to simplify the process of finding common denominators when adding or subtracting fractions with different denominators. By identifying the divisibility relationships between the denominators, you can determine the least common multiple (LCM) more efficiently. For example, if the denominators are 6 and 9, you can use the divisibility rules to recognize that 6 is divisible by 2 and 3, while 9 is divisible by 3. This allows you to quickly identify the LCM of 18, which becomes the common denominator for the fractions. Applying the divisibility rules in this context can save time and reduce the complexity of working with fractions.

Related terms

Divisor:

The number by which another number is to be divided.

Dividend:

The number that is to be divided by the divisor.

Remainder:

The amount left over when one number is divided by another, which is not evenly divisible.