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Multiples of 2 characteristics:
At the end of the integer is 、...of the number.
Multiples of 3 characteristics:
The sum of the digits of an integer is a multiple of 3. For example, ......
Multiples of 5 characteristics:
At the end of an integer is a number of 0 or 5.
1) If the single digit of an integer is truncated, and then subtract 2 times the single digit from the remaining number, if the difference is a multiple of 7, then the original number.
Divisible by 7. If the difference is too large or the mental arithmetic is not easy to see whether it is a multiple of 7, you need to continue the above truncation, multiplication, subtraction, and test.
Poor process until it can be clearly judged. For example, the process of determining whether 133 is a multiple of 7 is as follows: 13 3 2 7, So.
Take 133 as a multiple of 7; Another example is the process of determining whether 6139 is a multiple of 7 as follows: 613 9 2 595
49, so 6139 is a multiple of 7, and so on.
2) If the single digit of an integer is truncated, and then 4 times the single digit is added to the remaining number, if the difference is a multiple of 13, then the original.
The number is divisible by 13. If the difference is too large or the mental arithmetic is not easy to see whether it is a multiple of 13, it is necessary to continue with the above truncated, doubled, and phase.
The process of adding and checking the difference until it can be clearly judged.
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2: As long as the end is 02468, the number is a multiple of 2.
5: As long as the number at the end of 05 is a multiple of 5.
3: The numbers on each digit add up to multiples of 3, and this number is a multiple of 3. Hope.
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The multiple feature of 2: the number of the single digit is the number of ; Multiples of 5: the single digit is 0 or the number of pure Qingdan; Multiples of 3: The sum of the numbers on each digit is a multiple of 3.
Multiplier is a mathematical term that refers to the product of a number and an integer.
An integer can be divisible by another integer, which 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 a number by another number.
For example, a b = c, that is, a is a multiple of b. 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, 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.
Mathematical formula (multiplier relationship).
1. The number of copies per conversation The number of copies = the total number of copies The number of copies = the number of copies The total number of copies = the number of copies per copy.
2. 1 multiple multiplier = several times several times 1 multiple = multiple = multiple multiple = multiple = 1 multiple.
3. Speed Time = Distance Distance Speed = Time Distance Time = Speed.
4. Unit price quantity = total price total price unit price = quantity total price quantity = unit price.
5. Work efficiency.
Working hours = total amount of work Total amount of work Productivity = Working hours Total amount of work Working hours = Productivity.
6. Factor Factor = Product One factor = another factor.
7. Dividend.
Divisor = Quotient Dividend Quotient = Divisor Quotient Divisor = Dividend.
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The multiple feature of 2: the number of the single digit is the number of ; Multiples of 5 characteristics: the single digit is 0 or 5 of the number of slag liquid consumption; Multiples of 3: The sum of the numbers on each digit is a multiple of 3.
So multiples of 2, 3, and 5 are multiples of 0, 5, and 3, and an integer is divisible by another integer, and that integer is a multiple of another integer.
For example, 15 can be 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.
The single digit is 0: because 2*5=10, this number must be a multiple of 10, so the single digit is 0.
All the numbers add up to multiples of 3: Because numbers that are multiples of 3 have the characteristic that all numbers add up to multiples of 3.
is a multiple of 30: because 2*3*5=30, this number must be a multiple of 30.
The minimum number is 30, for example, 90 is a multiple of 2, 3, 5.
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Characteristics of multiples of 2,3,5: Numbers that are 5 or 0 in the single digit are multiples of 5. The single digit is 0, and the numbers of 2, 4, 6, and 8 are all multiples of 2. The multiple of Liquid Punch 3 can be any number in the single digit.
The maximum two-digit number of multiples of 2,3,5: The maximum two-digit number of multiples of 2,3,5 at the same time is 90. The two digits that are multiples of 2,3,5 at the same time are , and in these three numbers, the largest two digits are 90, so it can be seen that the maximum two digits of multiples of 2,3,5 at the same time are 90.
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2.Multiples are characterized by even numbers.
The sum of the characteristic digits of multiples of 3 is a multiple of 3.
The characteristic single digit of a multiple of 5 is 5 or 0
Multiples are characterized by a single digit being 0 and the digit is divisible by 3.
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Multiples of 2 are characterized by a single digit being an even number, multiples of 3 being the sum of the digits being a multiple of 3, and multiples of 5 being a single digit being 0 or 5
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At the same time, the single digit is 0
And the sum of the numbers is a multiple of 3.
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The multiple of 2 is characterized by the fact that the single digit is , that is, an even number.
The multiple of 3 is characterized by the fact that the sum of the digits in each digit is divisible by 3.
The multiple of 5 is characterized by the fact that the single digit is 0 or 5
At the same time, the multiple feature of is that the single digit is 0, and the sum of the digits on each digit is divisible by 3.
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Characteristics of multiples of 2: Everybody is the number of .
Characteristics of multiples of 5: The single digit is an integer of 0 or 5.
Characteristics of multiples:
1. An integer can be divisible by another integer, and this integer is a multiple of another integer, such as 15 can be divisible by 3 or 5, so 15 is a multiple of 3 and a multiple of 5.
2. The quotient obtained by dividing one number by another number, such as a b=c, that is, a is a multiple of b, for example: a b=c, it can be said that a is c times of b.
3. There are infinite multiples of a number, that is to say, the set of multiples of a number is an infinite set, note: a number cannot be called a multiple alone, only who is the multiple of whom.
Note the difference between "multiple" and "multiple":
1. "Multiple" refers to the quantitative relation, which is based on the concept of multiplication and division.
For example, if there are 10 boys and 30 girls, because "10 3=30" or "30 10=3", it can be said that the number of girls (30) is three times the number of boys (10), and it can also be said that three times the number of boys (10) is equal to the number of girls (30).
"Times" actually represents the quotient of two numbers (this quotient can be an integer, a decimal, a fraction and other manifestations).
2. "Multiple" refers to the connection between numbers, which is based on the concept of divisible.
For example, 30 is divisible by 6, and 30 is a multiple of 6. It can be seen that "multiples" cannot exist independently (with specific directivity), and there are special requirements for the form of logarithms (it must be an integer), and at the same time, 30 is also 5 times of 6, because 6 5 30, "6 5" means 5 times of 6. Therefore, from this point of view, the meaning of "multiple" should be broadly defined as "multiple", which can be regarded as a manifestation of the former in a specific situation.
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Multiples of the characteristic:
Feature divisible by 2: even.
Divisible by 3: The sum of the digits on each bit is divisible by 3.
Divisible by 5 feature: A number that is 0 or 5 in the single digit.
At the same time, the characteristics that can be divisible: the single digit is 0 and the sum of the numbers on each bit is divisible by 3 Application and extension of knowledge points
As long as a number is divisible by both 2 and 3, then the number can be divisible by 6 The sum of the numbers in each digit is divisible by 9, then the number can be divisible by 9 Proposition**] Frequently Asked Question Type.
Example 1: The maximum three-digit number that can be divisible at the same time is.
Analysis: According to the question, you can first determine the characteristics of the number that can be divisible by 2, the characteristics of the number that can be divisible by 3, the characteristics of the number that can be divisible by 5, and then determine the characteristics of the number that can be divisible at the same time, and then calculate the largest three-digit number
Solution: Features divisible by 2: a number that is in the single digit, a feature of a number that is divisible by 3:
The sum of the numbers on each digit is divisible by 3 and the characteristics of a number that is divisible by 5: the number in the single digit is a number of 0 or 5, and to be divisible by 2 and 5 at the same time, the single digit of this three-digit number must be 0
To be divisible by 3 and to be the largest three-digit number, this number is 990 so the answer is: 990
Comment: This question mainly examines the characteristics of numbers that can be divisible at the same time Example 2: 104 at least plus.
can be divisible at the same time
Analysis: Numbers that are divisible at the same time must be characterized by the fact that the digits in one digit must be 0, and the sum of the digits in each digit is divisible by 3, so that 104 is at least plus 16
Solution: According to the analysis, 104 can only be divisible by adding at least 16 to be divisible at the same time so the answer is: 16
Comment: This problem is mainly solved according to the characteristics of numbers that can be divided at the same time
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Multiples of the characteristic:
Feature divisible by 2: even.
Divisible by 3: The sum of the digits on each bit is divisible by 3.
Divisible by 5 feature: A number that is 0 or 5 in the single digit.
At the same time, the characteristics that can be divisible: the single digit is 0 and the sum of the numbers on each bit is divisible by 3 Application and extension of knowledge points
As long as a number is divisible by both 2 and 3, then the number can be divisible by 6 The sum of the numbers in each digit is divisible by 9, then the number can be divisible by 9 Proposition**] Frequently Asked Question Type.
Example 1: The maximum three-digit number that can be divisible at the same time is.
Analysis: According to the meaning of the question, you can first determine the characteristics of the number that can be divisible by 2, the characteristics of the number that can be divisible by 3, the characteristics of the number that can be divisible by 5, and then determine the characteristics of the number that can be divisible at the same time, and then calculate the largest three-digit number
Solution: Features divisible by 2: a number that is in the single digit, a feature of a number that is divisible by 3:
The sum of the numbers on each digit is divisible by 3 and the characteristics of a number that is divisible by 5: the number in the single digit is a number of 0 or 5, and to be divisible by 2 and 5 at the same time, the single digit of this three-digit number must be 0
To be divisible by 3, and if it is the largest three-digit number, this number is 990 so the answer is: 990
Comment: This question mainly examines the characteristics of numbers that can be divisible at the same time Example 2: 104 at least plus.
can be divisible at the same time
Analysis: Numbers that are divisible at the same time must be characterized by the fact that the digits in one digit must be 0, and the sum of the digits in each digit is divisible by 3, so that 104 is at least plus 16
Solution: According to the analysis, 104 can only be divisible by adding at least 16 to be divisible at the same time so the answer is: 16
Comment: This problem is mainly solved according to the characteristics of numbers that can be divided at the same time
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