divisible

What is Divisible in Math? Definition

Divisibility is a fundamental concept in mathematics that refers to the ability of one number to be divided by another without leaving a remainder. In other words, if a number is divisible by another number, it means that it can be evenly divided by that number.

History of Divisible

The concept of divisibility has been studied and used in mathematics for thousands of years. Ancient civilizations such as the Egyptians, Babylonians, and Greeks recognized the importance of divisibility in various mathematical applications. The concept has been refined and expanded upon by mathematicians throughout history, leading to the development of more advanced theories and techniques.

What Grade Level is Divisible for?

The concept of divisibility is typically introduced in elementary school, around the third or fourth grade. It is an important foundational concept in number theory and arithmetic, and it continues to be used and expanded upon in higher-level math courses.

Knowledge Points of Divisible and Detailed Explanation

Divisibility involves several key knowledge points, including:

1. Dividend: The number being divided.
2. Divisor: The number by which the dividend is divided.
3. Quotient: The result of the division.
4. Remainder: The amount left over after division, if any.

To determine if a number is divisible by another number, we can use various rules and tests. Here are some common divisibility rules:

1. Divisible by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
2. Divisible by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
3. Divisible by 5: A number is divisible by 5 if its last digit is either 0 or 5.
4. Divisible by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

These rules can be applied step by step to determine if a number is divisible by another number.

Types of Divisible

There are various types of divisibility, including:

1. Divisibility by a single number: This refers to the ability of a number to be divided by a specific divisor without leaving a remainder.
2. Divisibility by multiple numbers: This refers to the ability of a number to be divided by multiple divisors without leaving a remainder.
3. Divisibility by a range of numbers: This refers to the ability of a number to be divided by any number within a given range without leaving a remainder.

Properties of Divisible

Divisibility exhibits several properties, including:

1. Reflexive property: Every number is divisible by itself.
2. Transitive property: If a number is divisible by another number, and that number is divisible by a third number, then the first number is divisible by the third number.
3. Distributive property: If a number is divisible by two other numbers, then it is divisible by their sum or difference.

How to Find or Calculate Divisible?

To determine if a number is divisible by another number, you can follow these steps:

1. Identify the divisor and dividend.
2. Apply the relevant divisibility rule(s) based on the divisor.
3. Check if the conditions of the rule(s) are met.
4. If the conditions are met, the dividend is divisible by the divisor.

Formula or Equation for Divisible

There is no specific formula or equation for divisibility. Instead, divisibility relies on rules and tests that are applied to determine if a number is divisible by another number.

How to Apply the Divisible Formula or Equation?

As mentioned earlier, there is no specific formula or equation for divisibility. Instead, you can apply the relevant divisibility rules and tests to determine if a number is divisible by another number.

Symbol or Abbreviation for Divisible

There is no specific symbol or abbreviation for divisibility. Instead, the concept is typically expressed using the terms "divisible" or "divisibility."

Methods for Divisible

There are several methods for determining divisibility, including:

1. Divisibility rules: These rules provide specific conditions that must be met for a number to be divisible by another number.
2. Prime factorization: By finding the prime factors of a number, you can determine if it is divisible by another number.
3. Long division: This method involves performing long division to determine if a number is divisible by another number.

Solved Examples on Divisible

Example 1: Is 246 divisible by 3? Solution: The sum of the digits of 246 is 2 + 4 + 6 = 12. Since 12 is divisible by 3, we can conclude that 246 is divisible by 3.

Example 2: Is 1,234 divisible by 6? Solution: The last digit of 1,234 is 4, which is even. However, the sum of the digits (1 + 2 + 3 + 4 = 10) is not divisible by 3. Therefore, 1,234 is not divisible by 6.

Example 3: Is 5,000 divisible by 10? Solution: The last digit of 5,000 is 0, which means it is divisible by 10.

Practice Problems on Divisible

1. Is 987 divisible by 9?
2. Is 3,456 divisible by 4?
3. Is 2,222 divisible by 7?

FAQ on Divisible

Question: What does it mean for a number to be divisible? Answer: A number is divisible if it can be divided by another number without leaving a remainder.