Number Systems and Divisibility Rules Numbers are a fundamental system of representation for quantity and order. They come in various forms, including wh...
Numbers are a fundamental system of representation for quantity and order. They come in various forms, including whole numbers, fractions, decimals, and negative numbers. These numbers can be combined and manipulated in various ways to express quantities and relationships.
Divisibility rules are set of guidelines that help us determine whether a number is divisible by a specific another number. These rules involve examining the remainder when a number is divided by another. Based on the remainder, we can categorize the number as divisible or not divisible by that specific number.
Common Divisibility Rules:
A number is divisible by 1 if and only if the remainder is 0 when it is divided by 1.
A number is divisible by 2 if and only if the remainder is 0 when it is divided by 2.
A number is divisible by 3 if and only if the remainder is 0 when it is divided by 3.
A number is divisible by 4 if and only if the remainder is 0 when it is divided by 4.
A number is divisible by 5 if and only if the remainder is 0 when it is divided by 5.
A number is divisible by 6 if and only if it is divisible by both 2 and 3.
Examples:
12 is divisible by 1 because the remainder is 0 when it is divided by 1.
18 is divisible by 2, 3, and 4 because the remainders are 0 when it is divided by these numbers.
21 is divisible by 3 but not divisible by 5 because the remainder is 1 when it is divided by 5.
30 is divisible by 6 because it is divisible by both 2 and 3.
45 is divisible by 1, 3, and 5 because the remainders are 0 when it is divided by these numbers.
Conclusion:
Understanding number systems and divisibility rules is crucial for developing a strong foundation in quantitative aptitude. By mastering these concepts, students can apply them to solve various problems involving numerical quantities and relationships