What is a divisor What is a multiple Specific definition

Definition The integer a is divided by the integer b(b≠0).

The quotient obtained by division is exactly an integer without a remainder, so we say that a is divisible by b, or b is divisible by a multiple of b, and b is called the divisor (or factor) of aBefore college, the term was generally a positive divisor. Divisors and multiples are interdependent, and it cannot be said that a certain number is a divisor or multiple alone.

The divisor of a number is finite.

Example Within the range of natural numbers, the divisor of 6 has

There is an approximate number of 10

There is an approximate number of 15

Note: The divisor of a number includes 1 and itself. For example, 24 is divisible so the divisor of 24 is

The greatest common divisor of this paragraph If a number c is both a divisor of a number A and a divisor of a number B, then c is called the common divisor of a and b. It can be expressed as (a,b)=c.

Greatest common divisor The greatest common divisor of two numbers is called the greatest common divisor of these two numbers.

Finding the greatest common divisor 1,

Enumeration. List the divisors of the two numbers one by one, find the common divisor from them, and then find the largest one from the common divisor, that is, the greatest common divisor of these two numbers. Example:

Find the greatest common divisor between 30 and 24. The approximate number of 30 is: 1, 2, 3, 5, 6, 10, 15, 30

The divisor of 24 is: 1, 2, 3, 4, 6, 8, 12, 24 It is easy to get the greatest common divisor of 6, so the greatest common divisor of 30 and 24 is 6

Divisor: If an integer is divisible by two integers, then the number is the divisor of two numbers. Divisors are finite and generally use the greatest common divisor.

Multiples: If both numbers can be divisible by an integer, then this number is the common multiple of these two numbers, and there are infinite multiples of two numbers, generally using the least common multiple.

An integer can be divisible by another integer, then that integer is a multiple of another integer.

If a number c is both a factor of a and a factor of b, then c is called the common factor of a and b.

The largest common factor of two numbers is called the greatest common factor of these two numbers.

Multiples that are common to two or more integers are called their common multiples.

The smallest of the common multiples of two or more integers is called their least common multiple.

Multiplier features:If the single digit of an integer is truncated, and then 2 times the single digit is subtracted from the remaining number, if the difference is a multiple of 7, the original number is divisible by 7. If the difference is too large or it is not easy to see whether it is a multiple of 7, the above process of truncating, multiplying, subtracting, and checking the difference will be carried out until it can be clearly determined.

For example, the process of determining whether 133 is a multiple of 7 is as follows: 13-3 2=7, so 133 is a multiple of 7; Another example is the process of determining whether 6139 is a multiple of 7 as follows: 613-9 2=595, 59-5 2=49, so 6139 is a multiple of 7, and so on.

Divisor, also known as factor, the integer a divided by the integer b(b≠0), the quotient obtained by division is exactly an integer without a remainder, it is said that a can be divisible by b, or b is divisible by a multiple of b, and b is called the divisor of a. An integer can be divisible by another integer, which is a multiple of another integer.

Characteristics of multiples:

multiples of . At the end of a number is an even number (0,2,4,6,8), and this number is a multiple of 2.

multiples of . The sum of the digits of a number is a multiple of 3, and this number is a multiple of 3.

multiples of . The last two digits of a number are multiples of 4, and this number is a multiple of 4.

multiples of . If a number ends with 0 or 5, this number is a multiple of 5.

multiples of . As long as a number is divisible by both 2 and 3, then the number is divisible by 6.

What are multiples, factors, divisors, and the relationships between them.

1. Multiples refer to the situation where one number is divisible by another number, and the other number is called a multiple of this number. For example, 6 is a multiple of 3 because 6 is divisible by 3. 2. A factor is a number that is divisible by a number.

For example, 2 and 3 are factors of 6 because they are both divisible and divisor refers to a positive integer factor that is divisible by a number. For example, the divisor of 6 is , and 6 itself. Multiples and factors are relative concepts.

If one number is a multiple of another, then the other number must be a factor of that number. If one number is a factor of another number, then the other number must be a multiple of this number. Also, all the divisors of a number are the factors of that number, whereas all the factors of a number are not necessarily its divisors.

Definition. In elementary mathematics, when two positive integers are multiplied, then both numbers are called the factor of the product, or divisor.

Definition of Primary Mathematics: If a*b = c (a, b, c are all integers), then we call a and b the factors of c. It should be noted that this relationship is only true when the dividend, divisor, and quotient are all integers and the remainder is zero.

Conversely, we call c a multiple of a and b. When looking at factors and multiples, 0 is not considered in elementary school mathematics.

In fact, the factor is generally defined as an integer: let a be an integer, b be a non-zero integer, and if there is an integer q such that a=qb, then b is a factor of a, denoted as b|a。But there are also authors who do not ask for b≠0.

For example: 2x6 = 12, the product of 2 and 6 is 12, so 2 and 6 are the factors of 12. 12 is a multiple of 2 and a multiple of 6.

3x(-9) = -27, and both 3 and -9 are factors of -27. -27 is a multiple of 3 and -9.

Generally speaking, multiply the integer a by the integer b to get the integer c, and both the integer a and the integer b are called the factors of the integer c, and conversely, the integer c is a multiple of the integer a and a multiple of the integer b.

Explanation of the divisor.

The word decomposition of the word about the interpretation of the covenant (covenant) ē rope. Restraint, Restriction : Restraint .

Covenant. Restricting. Conventional.

Mutually agreed terms to be followed: Contractual. Treaty.

Indenture. The matter is decided first: make an appointment.

Appointment. Invitation: Invitation.

About the set. Thrifty: Saving.

Frugal. Brief, simple: return to the appointment by Bo.

Explanation of the simple number of numbers (数) ù the quantity that represents, divides, or is calculated: the number. Quantity.

Numeral. Number theory (a branch of mathematics that studies the properties of positive integers and the laws related to them). Numerical control.

Few, Zheng Li several: several people. days.

Technique orange bush shouting art, academic: "The number of today's husband is the number, and the decimal is also". Destiny, day.

Multiple. An integer can be divisible by another integer, and that integer is a multiple of another integer. For example, 15 is divisible by 3 or 5, so 15 is a multiple of 3 and a multiple of 5.

The quotient obtained by dividing one number by another. For example, a b c means that a is a multiple of b and a is a multiple of b.

3 If a factor is divisible by its product, then this number is a factor, and its product is a multiple.

Factor 1 Factor 2 Multiple.

For example, if a b=c, it can be said that a is c times that of b.

There are infinite multiples of a number (except 0), which means that the set of multiples of a number is an infinite set.

Note: You can't call a number a multiple alone, you can only say who's the multiple.

Approximate. The integer a is divisible by the integer b, a is called a multiple of b, and b is called the divisor of a (now the new textbook is called a factor).

in the range of natural numbers).

There is an approximate number of 6

There is an approximate number of 10

There is an approximate number of 15

Note: The divisor of a number includes 1 and itself.

The quotient of the integer a divided by the integer b(b≠0) is exactly an integer without a remainder, so we say that a is divisible by b, or b is divisible by a multiple of b, and b is a divisor or factor of a. Divisors and multiples are interdependent, and it cannot be said that a certain number is a divisor or multiple alone.

Divisor: If an integer is divisible by two integers, then those two numbers are the divisors of the number. Approximation is finite, and the approximate number is generally used. To put it bluntly: a divisor is a divisor that is divisible by it.

For example, there are those that are divisible by 24

So the divisor of 24 has

A divisor is a number that is divisible by this number, generally less than or equal to it (including itself).

Greatest common divisor: If a number is both a divisor of a number a and a divisor of a number b, it is called the divisor of a, b, and the divisor of a, b.

The largest of , which can include a, b itself, is called the greatest common divisor of a,b.

In the same way, the smallest of the common multiples of a and b is called the least common multiple of a and b.

If the integer a is divisible by the integer b (b is not 0), then a is said to be a multiple of b and b is the divisor of a.

Problem solving process] e.g. 6 3 2, then 3 is the divisor of 6.

Note: Divisors and multiples exist with each other, and it cannot be said that a certain number is a factor alone.

Multiples and divisors

Greatest common divisor: The common divisor of several numbers, which is called the common divisor of these numbers. There is a finite number of common factors. The largest of these is called the greatest common divisor of these numbers.

Least common multiple: The common multiple of several numbers, which is called the common multiple of these numbers. There are infinite common multiples. The smallest of these is called the least common multiple of these numbers.

Co-prime: Two numbers with a common divisor of only 1 are called coprimes. The two numbers that are adjacent to each other must be coquainous. Two consecutive odd numbers must be coprime with each other. 1 and any number is co-prime.

General fraction: The distinction of different denominator fractions into fractions with the same denominator as the original fraction is called universal fraction. (The lowest common multiple is used for general division).

Reduction: Divide the numerator and denominator of a fraction by the common divisor at the same time, and the fractional value remains unchanged, this process is called reduction.

Simplest fraction: The fraction whose numerator and denominator are coprime numbers is called the simplest fraction. At the end of the calculation, the resulting number must be reduced to the simplest fraction.

Prime number (prime number): A number that has only two divisors of 1 and itself is called a prime number (or prime number).

Composite: A number that is called a composite number if it has a divisor other than 1 and itself. 1 is not a prime number, nor is it a composite number.

Prime factor: If a prime number is a factor of a number, then this prime number is that of that number'Prime factor.

Decomposing prime factors: Expressing a composite number in terms of prime factors is called decomposing prime factors.

Multiplier features:

A characteristic of multiples of 2: Everybody is 0,2,4,6,8.

Characteristics of multiples of 3 (or 9): The sum of the numbers on each digit is a multiple of 3 (or 9).

A characteristic of the multiple of 5: Everybody is 0, 5.

Characteristics of multiples of 4 (or 25): The last 2 digits are multiples of 4 (or 25).

Characteristics of multiples of 8 (or 125): The last 3 digits are multiples of 8 (or 125).

Characteristics of multiples of 7 (11 or 13): The difference (large-small) between the last 3 digits and the rest of the digits is a multiple of 7 (11 or 13).

Characteristics of multiples of 17 (or 59): The difference between the last 3 digits and the remaining 3 times (large - small) is a multiple of 17 (or 59).

Characteristics of multiples of 19 (or 53): The difference between the last 3 digits and the remaining 7 times (large-small) is a multiple of 19 (or 53).

Characteristics of multiples of 23 (or 29): The difference between the last 4 digits and the remaining 5 times (large - small) is a multiple of 23 (or 29).

The greatest common divisor is the smaller number and the least common multiple is the larger number.

The greatest common divisor is 1 and the least common multiple is the product.

The two numbers are divided by their greatest common divisor, and the resulting quotient is mutually qualified.

The product of two numbers and the least common multiple is equal to the product of these two numbers.

The common divisor of two numbers must be the divisor of the greatest common divisor of these two numbers.

1 is neither prime nor composite.

Remove prime numbers greater than 3 with 6, and the result must be 1 or 5.