For example, 5 pairs of co prime numbers must be co prime numbers don t talk nonsense if you don t

1 and 50 6 and 7 9 and 10 11 and 13

What are coprime numbers between 8 and 9?

If two numbers have only a common divisor of 1, then the two numbers are coprime. ”

As can be seen from the concept, "coexistence" refers to a relationship between two numbers. We can't just say that a number is coprime.

How to tell if two numbers are coprime or not?

1) 1 and any natural number are coprime numbers.

We know that 1 is only an approximate 1; So no matter which natural number 1 is associated with, they all have only a common divisor of 1. So "1 and any natural number are co-primes." ”

2) Two adjacent natural numbers are coprimes.

There is an entry in the nature of divisible: "The common divisor of two numbers should be divisible by the sum and difference of these two numbers." ”

Two adjacent natural numbers, the difference between them is 1. And only 1 is divisible by 1, so these two adjacent natural numbers have only a common divisor of 1. Then "two adjacent natural numbers should be coprimes".

3) Two prime numbers that are not identical are also co-primes.

What is a "prime number"? As you all know, there are only two divisors of 1 and itself.

These two are not the same prime numbers, and they both have only two divisors: one is 1 and the other is itself. So these two different prime numbers have only a common divisor of 1. So "two prime numbers that are not identical are coprime numbers." ”

4) In addition to the three cases mentioned above, the other situations require us to make some necessary calculations to judge.

For example, determine whether 34 and 51 are coprime.

We can first decompose the smaller number into prime factors, and then see if the prime factors of the smaller number can be divisible by the larger number.

If the prime factors of the smaller number are not divisible by the larger number, then the two numbers are coprimes.

If the prime factors of the smaller number are divisible by the larger number, then the two numbers are not coprime.

2 and 7, 3 and 10, 13 and 19, 5 and 21, and two adjacent non-zero natural numbers.

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 are co-primes.

Prime numbers must be co-prime between them, and composite numbers may also be co-prime numbers between them. The so-called "co-prime number" is about the relationship between two or more numbers, rather than looking at some numbers individually or partially.

In other words, "co-prime" does not require that each of these numbers must be prime, as long as the common factor of two or more numbers is only 1, these two or more numbers are called "co-prime".

Co-prime number is a conceptual definition of two numbers that have a certain relationship in mathematics, which refers to the fact that there is only one number 1 in the common factor between two non-zero natural numbers, then we can say that these two numbers are co-prime, for example, the natural number 2 and the natural number 3 are co-prime numbers.

Through observation, we can find that two pairs of odd numbers adjacent to each other must be co-prime numbers, such as the number 3 and the number 5, and the greatest common divisor between the two numbers is 1, so it can be said that 3 and 5 are co-prime numbers. In addition, according to the definition of co-prime, we can also conclude that any natural number with the number 1 and any non-0 is a coprime.

In addition, we can also find that two natural numbers that are adjacent and non-zero must be coprime. For example, 3 and 8 are all coprime numbers. In the study of mathematics, it is very helpful for us to correctly find the least common multiple and the greatest common divisor between two natural numbers.

Two numbers with a common factor of only 1 are called coprimes. [Simple].

For two numbers, two numbers with a common factor of only 1 are called co-prime numbers. [For multiple numbers (textbook definition)] Several positive integers with the greatest common factor of only 1 are called coprime numbers.

Expression and use of attention.

1) The "two numbers" here refer to all natural numbers except 0. (2) "The common factor is only 1" should not be mistaken for "there is no common factor." 3) There are two different cases of coprime of three or more natural numbers:

One is that these natural numbers that are coprime are coprime in pairs. As. The other is not a pair of two.

As. When two positive integers (n) have no common divisor other than 1, they are said to be coprime. The probability of a coprime number is 6 2

This paragraph summarizes the methods for determining coprime numbers.

Direct resolution. 1) Two different prime numbers must be coprime numbers. For example, 2 is the same as 19. (2) Two adjacent natural numbers are coprime numbers.

For example, 15 vs. 16. (3) Two adjacent odd numbers are coprime numbers. For example, 49 vs. 51.

4) A large number is a prime number, and two numbers are co-prime numbers. For example, 97 vs. 88. (5) A decimal number is a prime number, and two numbers that are not multiples of decimal numbers are co-prime numbers.

For example, 7 and 16. (6) 2 and any odd numbers are coprime numbers. For example, 2 and 87.

7) 1 and any natural number (except 0) are coprime numbers.

Computational judgment method.

1) Both numbers are composite numbers (the difference between the two numbers is large), all the prime factors of the decimal number are not the divisor of the large number, and these two numbers are co-prime numbers. For example, 357 and 715, 357 = 3 7 17, and 17 are not divisors of 715, these two numbers are coprime. (2) Both numbers are composite numbers (the difference between the two numbers is small), and all the prime factors of the difference between these two numbers are not divisors of decimals, and these two numbers are coprime numbers.

Such as 85 and 78. 85 78 = 7, 7 is not a divisor of 78, these two numbers are coprime. (3) Both numbers are composite numbers, and all prime factors of a large number divided by the remainder of a decimal number (not "0" and greater than "1") are not divisors of decimals, and these two numbers are coprimes.

For example, 462 and are not divisors of 221, these two numbers are coprime. (4) Subtraction and division.

Such as 255 and 182. 255 182=73, observations 73<182. 182 (73 2)=36, apparently 36<73.

73－（36×2）=1， （255，182）=1。So these two numbers are co-prime. Application of Coprime Numbers Coprime numbers are a very important subject in mathematics, which will be learned in the sixth grade of primary mathematics, and will also appear in the Olympiad, which is very important!

Complex].

Two adjacent numbers are prime numbers with each other, and the two numbers have only a common factor of one and the two factors themselves are coprimes.

Two numbers with a common factor of only 1 are called coprimes.

If the factors of two numbers are not the same (except for 1), they are called coexistence.

Good luck with your studies!

1) Two different prime numbers must be coprime numbers. For example, 2 is the same as 19. (2) Two adjacent natural numbers are coprime numbers.

For example, 15 vs. 16. (3) Two adjacent odd numbers are coprime numbers. For example, 49 vs. 51.

4) A large number is a prime number, and two numbers are co-prime numbers. For example, 97 vs. 88. (5) A decimal number is a prime number, and two numbers that are not multiples of decimal numbers are co-prime numbers.

For example, 7 and 16. (6) 2 and any odd numbers are coprime numbers. For example, 2 and 87.

7) 1 and any natural number (except 0) are coprime numbers.

Two numbers with a common factor of only 1 are called coprimes.

There are many ways to judge whether two books are co-prime, look at this ** and say a little bit of my own understanding, in fact, it is very simple, just decompose these two factors and see if the factors are repeated.

Two different prime numbers must be co-prime numbers.

1. Coprime number is a concept in mathematics, that is, a non-zero natural number with only 1 in the common cause of two or more integers. Two non-zero natural numbers with a common factor of 1 are called coprimes.

and any god fighting natural numbers are co-prime, two different prime numbers are co-prime; A swimming grinding of a prime number and a composite number, these two numbers are not multiples of each other; Two composite numbers that do not contain the same prime factor are coprime of each other.

1. Two numbers with a common factor of only 1 are called coprime numbers (not counting themselves).

2. The two natural numbers with the most balanced common coarse and coarse concurrent factor is 1, which are called coprime numbers. Again, two numbers are the greatest common factor, and only 1 is a coprime number. By "two numbers" we mean all natural numbers except 0.

The common factor is only 1", and it cannot be mistaken for "there is no common factor." ”

3. Both numbers are composite, that is, there are divisors other than 1 and itself, such as 8, 9, 15 and other rock barriers;

Coprime means that the greatest common divisor of two composite numbers is 1, such as 8,9 and 8,15 are the composite numbers of two pairs of coprime.

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 are co-primes.

and any natural number coprime it. 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 of each other.

5. Any two adjacent numbers are co-prime;

6. The probability of their mutual quality (the greatest common divisor is one) is 6 2.