0 is not an even number, and a reason needs to be said

In an integer, the number divisible by 2 is even, and vice versa, the even number can be represented by 2k, and the odd number can be represented by 2k+1, where k is an integer. In elementary school arithmetic, we know that a number divisible by 2 is called an even number, and it is also commonly called a double number; Numbers that are not divisible by 2 are called odd numbers and are often called singular numbers.

Is 0 an odd number, or is it an even number? At that time, we talked about odd and even numbers, which generally meant those within the range of natural numbers. 0 is not a natural number, so there is no talk.

Is it possible to find out if 0 is an odd number or an even number? What we are: can be studied, and should be studied.

Not only should we study the integer 0, which is the only non-natural number that we have learned in arithmetic, but we should also expand the essentials of odd and even numbers to negative integers after learning algebra in middle school. The criterion for judging is also very simple, everything that is divisible by 2 is an even number, and what cannot be divisible by 2 is an odd number. Divisibility means that the quotient should be an integer, and there is no remainder.

Obviously, because 0 divided by 2 equals 0, the quotient is an integer 0, so 0 is even. Similarly, in integers, -2, -4, -6, -8, -10, -360, -2578, and so on, are all even; And -1, -3, -5, -7, -249, -1683, etc., are all odd numbers.

No, it's neither even nor odd, it's natural.

Yes, everything that is divisible by 2 is an even number.

0 is an even numberNumbers that are divisible by 2 and have no remainder are all even, and numbers that are not divisible by 2 are called odd. 0 is divisible by 2 and has no remainder, so 0 is even. If a number is a multiple of 2, it is an even number and can be expressed as 2n; If not, it is an odd number, which can be expressed as 2n+1 (n is an integer), i.e. the remainder of the odd number divided by two is one.

Even number nature: 1. Two consecutive integers must be an odd number and an even number.

2. The sum or difference between odd numbers and odd numbers is even; The sum or difference between an even and an odd number is an odd number; The sum of any number of even numbers is even; The sum of singular odd numbers is odd; The sum of even odd numbers is even.

3. The sum or difference of two odd (even) numbers is even; The sum or difference between an even number and an odd number must be an odd number.

4. All positive and even numbers except 2 are composite numbers.

5. The greatest common divisor of adjacent even numbers is 2, and the least common multiple is half of their product.

The properties of the number 0 are mainly as follows:

is the smallest natural number.

Divisible by any non-zero integer.

Not an odd number, but an even number (a special even number that is neither positive nor negative).

It's not a prime number, it's not a composite number.

It plays a placeholder role in multiple digits, such as 0 in 108 means that there is no place in the ten digits, and 18 must not be written.

It cannot be used as the highest digit of a single digit. However, some numbers need to be preceded by 0 to complete the full digits, etc.

0 is an even number, a number that is divisible by 2 and has no remainder, all are even, a number that is not divisible by 2 is called an odd number, and 0 is divisible by 2 and there is no remainder, so 0 is an even number. 0 is an integer between -1 and 1, the smallest natural number, and a rational number. 0 is neither positive nor negative, but the dividing point between positive and negative numbers.

Since odd and even numbers exist in natural numbers, and since zero is not a natural number, the question of whether zero is even is basically not discussed, and so on and so on are even numbers and other numbers are odd. There is no reciprocal of 0, the opposite of 0 is 0, the absolute value of 0 is 0, the square root of 0 is 0, the cube root of 0 is 0, 0 times any number is equal to 0, and the power of 0 of any number other than 0 is equal to 1.

1. According to the national standard: In January 2002, China's primary and secondary school mathematics textbooks were revised, stipulating that 0 is also a natural number. At the beginning of the founding of the People's Republic of China, due to the influence of some foreign countries, the textbooks of primary and secondary schools at that time had always stipulated that the natural number did not include 0

However, at present, some developed countries stipulate that 0 is also a natural number (first initiated by France).In order to facilitate international exchanges, the 1993 National Standards of the People's Republic of China also stipulate that natural numbers include 0

2. According to the definition of factors and multiples: a number is divisible by another number, and this number is a multiple of another number. 0 divided by any number other than 0 gives 0 with no remainder. So, 0 is a multiple of any non-zero natural number.

3. According to the definition of even numbers (Lujiao version): In natural numbers, multiples of 2 are even numbers. Then 0 is an even number.

Fourth, according to the range: in the range of natural numbers, the minimum even number is 0; In the range of positive integers, the smallest even number is 2; In the negative range, there is no minimum even number.

5. According to the research value: because any non-zero natural number is a factor of 0. However, considering that in the future study of the greatest common factor and the least common multiple, if 0 is not excluded, many problems cannot be discussed, for example, the discussion of the greatest common factor of 0 and 5 has neither practical nor mathematical significance, and for example, if 0 is taken into account, the least common multiple of any two natural numbers is 0, such a study has no value.

Therefore, the textbook points out that the content of the study in this unit refers to natural numbers (except 0), so as to avoid some unnecessary troubles.

6. According to the question: "What is the smallest even number?" Answer: The smallest even number is "0".

But ask "What is the smallest even number?" "It's not a good topic, what is it going to examine? For the sake of research convenience, we don't study 0 in primary school for the time being, but 0 is also an even number, and there are even numbers in negative numbers.

The topic itself does not examine the essential concept of even numbers. In order to avoid some unnecessary trouble, we can ask the question like this: What is the smallest even number in 1-20?

Explain the range of values clearly, and the answer will be concise and clear.

In integers, the number that can be divisible by 2 is called an even number, also known as a double number.

Even numbers include positive even numbers, wisdom hole negative even numbers, and 0

All integers are either odd (also known as singular) or even. When n is an integer, an even number can be expressed as 2n (n is an integer); Odd numbers can be expressed as 2n+1 (or 2n-1).

In the decimal system, we can determine whether the number is odd or even by looking at the single digit: the number file with the single digit is 1, 3, 5, 7, and 9 is guessed as an odd number; Numbers with single digits of 0, 2, 4, 6, and 8 are even.

In integers, the number that can be divisible by 2 is called an even number, also known as a double number, 0 divided by 2 equals 0, so 0 is divisible by 2, therefore, 0 is an even number.

0 is an even number。Numbers that are divisible by 2 and have no remainder are all even, and numbers that are not divisible by 2 are called odd. 0 is divisible by 2 and has no remainder, so 0 is even.

If a number is a multiple of 2, it is an even number and can be expressed as 2n; If not, it is an odd number, which can be expressed as 2n+1 (n is an integer), i.e. the remainder of the odd number divided by two is one.

Even-numbered nature

1) Two consecutive integers must be an odd number and an even number;

2. The sum or difference between odd numbers and odd numbers is even; The sum or difference between an even and an odd number is an odd number; The sum of any number of even numbers is even; The sum of singular odd numbers is odd; The sum of even odd numbers is even.

3. The sum or difference of two odd (even) numbers is even; The sum or difference between an even number and an odd number must be an odd number.

4. All positive and even numbers except 2 are composite numbers.

5. The greatest common divisor of adjacent even numbers is 2, and the least common multiple is half of their product.

6) The product of odd and odd numbers is odd; The product of an even number to an even number is an even number; The product of odd and even numbers is even;

7) The single digit of the even number must be or 8; The odd number must be in the single digit or 9;

8) No odd number is equal to any even number; the product of several integers, if there is an even number in them, the product must be even;

9) The square of even numbers is divisible by 4, and the square of odd numbers is divided by 8 by 1.

0 is an even numberNumbers that are divisible by 2 and have no remainder are all even, and numbers that are not divisible by 2 are called odd. 0 is divisible by 2 and has no remainder, so 0 is even.

If a number is a multiple of 2, it is an even number and can be expressed as 2n; If not, it is an odd number, which can be expressed as 2n+1 (n is an integer), i.e. the remainder of the odd number divided by two is one.

Even-numbered nature

1) Two consecutive integers must be an odd number and an even number;

2. The sum or difference between odd numbers and odd numbers is even; The sum or difference between an even and an odd number is an odd number; The sum of any number of even numbers is even; The sum of singular odd numbers is odd; The sum of even odd numbers is even.

3. The sum or difference of two odd (even) numbers is even; The sum or difference between an even number and an odd number must be an odd number.

4. All positive and even numbers except 2 are composite numbers.

5. The greatest common divisor of adjacent even numbers is 2, and the least common multiple is half of their product.

6) The product of odd and odd numbers is odd; The product of an even number to an even number is an even number; The product of odd and even numbers is even;

7) The single digit of an even number must be or 8; The odd number must be in the single digit or 9;

8) No odd number is equal to any even number; the product of several integers, if there is an even number in them, the product must be even;

9) The square of even numbers is divisible by 4, and the square of odd numbers is divided by 8 by 1.

0 is an even numberIn the range of natural numbers, the smallest even number is 0.

According to the definition of odd and even numbers: if a number is a multiple of 2, it is an even number (even number), which can be expressed as 2n; If not, it is an odd number (singular), which can be expressed as 2n+1 (n is an integer), i.e. the remainder of the odd number (singular) divided by two is one.

0=2*0, so 0 is an even number.