Is it right that two prime numbers must be mutually prime, and that two composite numbers must not b

A coprime number is two numbers that have no common divisor other than 1, called coprime, and a prime number is a number that has no divisor other than 1 and itself.

Therefore, "two prime numbers must be mutually prime" is true;

However, although both composite numbers have other divisors, they do not necessarily have a common divisor, so the two composite numbers may also be cogenetic. The second half of the sentence is incorrect.

Two prime numbers must be coprime because the factor only has 1 and itself, while two composite numbers are not necessarily cozy, such as 4 and 9, 4 and 13, and so on.

Second floor! 13 is a prime number!

Two prime numbers must be mutually prime, and two composite numbers must not be mutually primary. Wrong.

4 and 9 are both composite numbers.

But mutual. There are also adjacent numbers, such as (8, 9) 8 and 9 are composite numbers.

But mutual.

The previous sentence is definitely true.

The latter ones are not necessarily, for example, 8 and 9 are obviously not.

Two prime numbers, prime numbers have no factor, so the first half of the sentence is correct; In the second half of the sentence, if two composite numbers are adjacent numbers, it is impossible not to be mutually qualitative, you can try it yourself.

Obviously wrong, the first half of the sentence is right. The second half of the sentence is wrong, such as 4 and 9

There is no doubt that two prime numbers must be mutually prime.

But it is also possible that two composite numbers are coprime because each composite number may have a different factor.

Two prime numbers must be mutually prime, and two composite numbers must not be mutually primary. Wrong.

are all composite numbers. But mutual.

The two composite numbers must not be mutually qualitative, wrong!

When you are faced with these problems, you can give a few examples of them yourself, so that you can easily know if it is correct or not!

It is not necessary that two coprime numbers are prime numbers, as long as the common factor of two numbers is only 1, they are both coprime numbers.

There are three cases of two numbers of coprime:

Type 1: Both numbers are prime. For example, 3 and 5 are coprime numbers.

The second type: a prime number, a composite number. For example, 7 and 8 are coprime numbers.

The third type: both are composite numbers. For example, 14 and 15 are also coprime numbers.

Two prime numbers must be co-prime, but two coprime numbers are not necessarily prime.

Solution: The common factor of two numbers is only 1, and these two numbers are called coprime.

Two numbers that are coprime must be prime numbers, this statement is false.

For example, 5 and 9 are coprime, but 9 is a composite number, not a prime number.

The common factor of two different prime numbers is only 1, so two different prime numbers must be co-primes, which is true;

But two composite numbers may also be co-prime numbers, such as 8 and 9, 4 and 9 are both composite numbers, but they only have a common factor of 1, so they are coprime So two different composite numbers must not be coprime numbers

Combining two different prime numbers must be co-primes, and two different composite numbers must not be co-primes, which is wrong

So the answer is: false

1) Two prime numbers that are not the same must be co-primes. For example, 7 and 31 are coprime numbers.

2) Two consecutive natural numbers must be coprime. For example, 4 and 14 are coprime numbers.

3) Two odd numbers next to each other must be coprimes. For example, 5 and 77 are coprime numbers.

4) 1 and all other natural numbers must be coprimes. For example, 1 and 13 are coprime numbers.

5) 2 and any odd number are coprime numbers. For example, 2 and 9 are both coprime numbers.

6) An odd number and an even number with a prime factor of only 2 are co-primes. For example, 9 and 8 are both coprime numbers.

7) The larger of the two numbers is a prime number, and these two numbers must be co-prime. For example, 3 and 97 are large coprime numbers.

8) The smaller of the two numbers is a prime number, and the larger number is a composite number and is not a multiple of the smaller number, and the two numbers must be mutually parched prime numbers. For example, 2 and 54 are coprime numbers.

9) If the larger number is more than 1 or less than 1 than the small number by 2 times, these two numbers must be coprime hands or eggplant. For example, 13 and 25 are coprime numbers.

Hope it helps.

Have fun.

The common factor of two different prime numbers is only 1, so two brothers must be co-prime when they weigh different prime numbers, which is correct;

But two composite numbers may also be mutual orange prime numbers, such as 8 and 9, 4 and 9 are both composite numbers, but they only have a common factor of 1, so they are coprime numbers;

Therefore, two different composite numbers cannot be co-primes, and two different composite numbers must not be co-primes

Therefore, the answer to the case of the dust group is: false

Yes. Two different prime numbers must be co-prime numbers. Such as 2 and 3, 5 and 7.

The two numbers of a coprime are not necessarily prime. Such as 8 and 9, 11 and 12. Coprime numbers are a concept in mathematics that is a non-zero natural number in which the common factor of two or more integers is only 1.

Two non-zero natural numbers with a common factor of 1 are called coprimes.

Coprime numbers have the following theorem.

1) Two non-zero natural numbers with a common factor of only 1 are called coprimes; For example: 2 and 3, the common factor is only 1, which is a co-prime number;

2) A positive integer with the greatest common factor of only 1 for multiple numbers is called a coprime number;

3) Two different prime numbers, which are co-prime numbers;

4) 1 and any natural number are coprime. Two different prime numbers are coprime over each other. A prime number and a composite number, these two numbers are not multiples when they are mutually primitive. two composite numbers that do not contain the same prime factor are coprime;

5) any adjacent two numbers are coprime;

6) The probability of their coprime (the greatest common divisor is one) is 6 2

I looked through some materials and found that many articles say that "two prime numbers must be mutually prime", so why are so many people convinced of this law? I consulted a few teachers, and their reasons were twofold: first, the use of various newspapers and magazines to say this; Second, the so-called "two prime numbers" means two different prime numbers.

The correctness of this conclusion is obvious. In this regard, the author does not dare to agree. Let me explain it from two aspects.

From the connotation of "two prime numbers", two prime numbers should include two types of the same prime number and two different prime numbers. Like 3 and 5 are two prime numbers, while 2 and 2 one can also be called two prime numbers. Some teachers only take one of the understandings of one or the other, which is one-sided, and inevitably makes the mistake of narrowing the extension of the concept.

From the perspective of the arrangement of the textbook, the arrangement of the concept of "co-prime" is mainly to serve the teaching of the greatest common divisor and the least common multiple (of course, the establishment of the concept of the simplest fraction is also based on this).For illustrative purposes, let's look at an example: find the least common multiple of sum 36.

2}12 18 26 3}6 9 18 2!2 3.Meditha 1 33 requires the least common multiple of several numbers, which must be divided until they are mutually primary.

Except for this step, there are two identical prime numbers of 3 and 3. (Teaching practice shows that students often ignore this point and mistakenly believe that two Hunan homogeneous numbers are also co-prime.)

1. It is not necessary that both numbers of coprime are prime numbers. As long as the common factor of two numbers is only 1, they are coprime.

2. There are three cases of two numbers of coprime:

Type 1: Both numbers are prime. (e.g., 3 and 5 are coprime numbers) The second type: a prime number, a composite number. (e.g., 7 and 8 are coprime numbers) and the third type: both are composite numbers. For example, 14 and 15 are also coprime numbers.