Divisibility Rules Quiz

Study Notes

Rules For Divisibility

Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Divisibility by 10: A number is divisible by 10 if its last digit is 0.

Applications In Problem Solving

Determine whether a number can be evenly divided by another to solve fraction problems or simplify calculations.
Use divisibility rules to identify factors quickly when simplifying expressions or solving equations.
Apply in real-life scenarios, such as grouping items (e.g., packaging or scheduling) where equal distribution is needed.

Divisibility Tests

Practice testing numbers using the above rules:
- Example: Is 154 divisible by 2? Check last digit (4 → yes).
- Example: Is 123 divisible by 3? Sum of digits (1+2+3=6 → yes).
- Example: Is 100 divisible by 4? Last two digits (00 → yes).
Develop speed and accuracy in recognizing divisibility to improve mathematical efficiency.

Word Problems Involving Divisibility

Common forms:
- "If a number is divisible by X, find the smallest such number greater than Y."
- "How many items can be evenly distributed among a group without remainder?"
Strategy:
- Identify which divisibility rule applies.
- Break down the problem into manageable parts.
- Use algebraic expressions to represent quantities and apply divisibility principles.
Example Problem: "A baker has 36 cookies. How can he package them in boxes of 6?" (36 ÷ 6 = 6 boxes, confirming divisibility).

Rules For Divisibility

A number ends with an even digit (0, 2, 4, 6, 8) is divisible by 2.
The sum of a number's digits must be divisible by 3 for the number itself to be divisible by 3.
For a number to be divisible by 4, the last two digits of that number must form a value that is divisible by 4.
A last digit of either 0 or 5 indicates that a number is divisible by 5.
A number is divisible by 6 if it meets the criteria for both divisibility by 2 and by 3.
A last digit of 0 confirms that a number is divisible by 10.

Applications In Problem Solving

Divisibility rules are essential for simplifying fractions and calculations.
Quickly identifying factors simplifies expressions and aids in solving equations.
These concepts are applicable in practical situations like packing items or arranging schedules where even distribution is required.

Divisibility Tests

Practice recognizing divisibility through examples:
- For 154, the last digit is 4, thus it is divisible by 2.
- For 123, the sum of digits equals 6, making it divisible by 3.
- For 100, the last two digits are 00, confirming divisibility by 4.
Develop quick recognition of divisibility to enhance mathematical efficiency.

Word Problems Involving Divisibility

Common word problem formats include determining the smallest number divisible by a given value greater than another number, or calculating how many items can be evenly shared among a group.
To solve, identify the applicable divisibility rule, break down the problem, and utilize algebraic expressions for calculations.
Example: A baker has 36 cookies and can package them into boxes of 6, resulting in 6 boxes, thus confirming the divisibility of 36 by 6.

Description

Test your knowledge of the rules for divisibility by 2, 3, 4, 5, 6, and 10. This quiz will help you learn how to determine whether a number can be evenly divided by another, which is useful in solving fraction problems and simplifying equations. Perfect for practicing quick calculation skills.