Even Numbers

Definition

Even numbers are integers that can be exactly divided by 2, meaning they have no remainder when divided. These numbers include both positive and negative values, as well as zero, forming an essential subset of the integers. Even numbers are crucial in understanding patterns in mathematics, such as divisibility and parity, and they play a significant role in various mathematical operations and properties.

5 Must Know Facts For Your Next Test

1. Every even number can be expressed in the form of 2n, where n is an integer.
2. Zero is considered an even number because it can be divided by 2 without any remainder.
3. The sum of two even numbers always results in another even number.
4. The product of any integer and an even number will always yield an even number.
5. Even numbers are symmetrically distributed on the number line, appearing at regular intervals.

Review Questions

• How do you determine whether a number is even or not? Provide examples.
  • To determine if a number is even, check if it can be divided by 2 without leaving a remainder. For example, 4 is even because when you divide it by 2, you get 2 with no remainder. On the other hand, 5 is not even because dividing it by 2 results in 2 with a remainder of 1.
• What are some properties of even numbers when it comes to addition and multiplication?
  • When adding two even numbers together, the result is always another even number. For instance, adding 2 and 4 gives you 6, which is even. Similarly, when multiplying any integer by an even number, the product remains even. For example, multiplying 3 by 4 gives you 12, which is also even.
• Evaluate the significance of even numbers in the context of mathematical operations and their applications.
  • Even numbers hold great significance in mathematics due to their unique properties related to divisibility and arithmetic operations. Their predictable behavior in addition and multiplication simplifies many mathematical processes, making them essential for solving equations and understanding patterns. Additionally, in areas like computer science and programming, recognizing even and odd integers is critical for algorithms that require specific conditions based on parity.

Related terms

Odd Numbers: Odd numbers are integers that cannot be evenly divided by 2, resulting in a remainder of 1 when divided.

Integers: Integers are whole numbers that can be positive, negative, or zero, and include all even and odd numbers.

Divisibility: Divisibility refers to the ability of one integer to be divided by another without leaving a remainder.