What is a coprime number

Coprime numbers. Open Categories:

5th grade math.

Primary school mathematics textbooks define coprime numbers as follows: "Two natural numbers with only a common divisor and only 1 are called coprime numbers." ”

The "two numbers" here refer to natural numbers.

The common divisor is only.

1", which cannot be mistaken for "there is no common divisor." ”

Discriminant method: 1) Two different prime numbers must be co-primes.

For example, 2 is the same as 19.

2) If a prime number is not divisible by another composite number, the two numbers are coprime.

For example, 3 is the same as with.

3) 1 is not a prime number or a composite number, it is a coprime number together with any natural number. Such as 1 and 9908.

4) Two adjacent natural numbers are coprime numbers. As. 15 with.

5) Two odd numbers next to each other are coprime numbers. As. 49 with.

6) A large number is a prime number, and two numbers are co-prime numbers. Such as 97 and 88.

7) Decimals are prime numbers, and two numbers that are not multiples of decimal numbers are co-prime numbers. As. 7 and.

8) 2 and any odd number are coprime numbers. Such as 2 and 87.

9) Both numbers are composite numbers (the difference between the two numbers is large), and all the prime factors of the decimal number are not divisors of the large numbers, and these two numbers are coprime numbers.

For example, 357 and 715, 357 = 3 7 17, and 17 are not divisors of 715, these two numbers are coprime.

10) Both numbers are composite numbers (the difference between two numbers is smaller), all the prime factors of the difference between these two numbers are not divisors of decimals, and these two numbers are coprime. Such as 85 and 78.

85 78 7, 7 is not a divisor of 78, these two numbers are coprime.

11) Both numbers are composite, and the remainder of the large number divided by the decimal number (not "0" and greater than ").

1") All prime factors are not divisors of decimals, these two numbers are coprimes. As. 462 with.

Neither is a divisor of 221, and these two numbers are coprime.

12) Subtraction and division. Such as 255 and 182.

255 182 73, observed.

182 (73 2) 36, obviously.

So these two numbers are co-prime.

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.

Do you know what a coprime number is?

If there are only two numbersCommon divisor1, then these two numbers areCoprime numbers.

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.

The correct way to say it should be:

1 and 32 are coprime numbers.

8 and 9 are coprime numbers.

The difference between "co-prime" and "prime" is that:

"Prime number" refers to a class of numbers that are "only two divisors of 1 and itself". We can say that a certain number is prime. For example: 5 is a prime number.

"Coprime" indicates a relationship between two numbers.

Regularity judgment method

According to the definition of coprime numbers, some rules can be summarized, and these rules can be used to quickly determine whether a group of numbers is coprime or not.

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.

It must be a coprime number. For example, 4 and 14 are coprime numbers.

3) The two odd numbers of adjacent manuscripts 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) The larger of the two numbers is a prime number, and these two numbers must be co-prime numbers. For example, 3 and 19, space-based 16 and 97 are coprime numbers.

6) 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 these two numbers must be co-prime. For example, 2 and 54 are coprime numbers.

7) 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. For example, 13 and 25 are coprime 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 splits with a common knowledge factor of only 1 are called coprime numbers.

Coprime numbers are a concept in mathematics, i.e., non-zero natural numbers with a common factor of 1 for two or more integers. 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) Take out two positive integers and the probability of their mutual quality (the greatest common divisor is one), the first of which is 6 2.

Two natural numbers whose greatest common factor is 1 are called coprimes.

1) Two prime numbers that are not the same must be co-primes.

2) If a prime number is not divisible by another prime number, the two numbers are co-prime.

3) Two adjacent natural numbers are coprimes.

4) Two odd numbers next to each other are coprime numbers.

5) 2 and any odd number are coprime numbers.