Seven digit 13ab45c can be divided by 729, and the numbers on each digit are different from each other. How much is A.B.C equal to As above

Seven digit 13ab45c can be divided by 729, and the numbers on each digit are different from each other. How much is A.B.C equal to As above


729 = 8 × 9 × 11, that is, 13ab45c can be divisible by 8, 9, 11, and 8, so 400 + 50 + C must be divisible by 8, so C = 6.1 + 3 + A + B + 4 + 5 + C can be divisible by 9, a + B + C can be divisible by 9, and 5. A + B can be divisible by 9, and 8.1 + A + 4 + c-3-b-5 must be divisible by 11, that is, A-B + 3 can be divisible by 11



1. The concept of counting unit 2. A can be divided by B (B is not equal to 0) a is B () B is a ()?


1. Concept of counting unit
We usually use the decimal counting method, and the counting units are: one (one), ten, hundred, thousand, ten thousand, one hundred thousand For example: one, ten, one hundred, one thousand, ten thousand, one hundred thousand And so on. It's called the counting unit of numbers
One, ten, hundred, thousand, ten thousand They are all units of count
These counting units are arranged in a certain order, and the positions they occupy are called digits
The four counting units are: 0.001, unit, ten thousand, hundred million
2. A can be divided by B (B is not equal to 0) a is a multiple of B and B is a factor of A



How to find a small strategy for the factor of a number


When exploring the method of finding the factor of a number, in order to make students more vividly understand that "to find in a certain order" will not be repeated and omitted, this lesson uses the number axis diagram, through demonstrating the factor of 18 (one to one to the ground), students intuitively see the "order", and really realize that it is difficult for students to really



How to find the factor and multiple of a number


If you decompose a number into prime factors, you can get the factor of the number. Multiply 1,2 by the number to get the multiple of the number



How to find the factor of a number more convenient?


There is no shortcut to this problem. You can only get several prime numbers of this number by dividing the prime numbers of 2, 3, 5 and 7 one by one. For example, 870 is a number whose last digit is 0. You can divide it by 10 to get 87. 10 itself is 2 × 5. 87 △ 3 = 29, so 850 = 2 × 3 × 5 × 29



How to find the multiple of a number


Factor: first decompose the factor into prime number multiplication. A better example is: 36 = 2 ^ 2 * 3 ^ 2, and then arrange from each prime number to the highest power: 2 ^ 0 * 3 ^ 0 = 1 * 1 = 12 ^ 1 * 3 ^ 0 = 2 * 1 = 22 ^ 2 * 3 ^ 0 = 4 * 1 = 42 ^ 0 * 3 ^ 1 = 1 * 3 = 32 ^ 1 * 3 ^ 1 = 2 * 3 = 62 ^ 2 * 3 ^ 1 = 4 * 3 = 122 ^ 0 * 3 ^ 2 = 1 * 9 = 92 ^ 1 * 3 ^ 2



A number is both a factor and a multiple of 16. It has () factors


This number is 16, and its factors are 1, 2, 4, 8, 16
So a number is not only a factor of 16, but also a multiple of 16. This number has (5) factors



What is a two digit number, a factor of 80, a multiple of 5, or a multiple of 8?


"Is it a multiple of 5, or a multiple of 8" indicates that the number is a common multiple of 5 and 8
5. The least common multiple of 8 is 40
There are only two numbers, 40 and 80, which are factors of 80 and multiples of 40



A number is not only a multiple of 9, but also a factor of 54______ .


The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54; the multiples of 9 within 54 are: 9, 18, 27, 36, 45, 54; the multiples of 9 and 54 are: 9, 18, 27, 54; so the answer is: 9, 18, 27, 54



A number is not only a factor of 72, but also a multiple of 24


The multiple of 24 is: 24, 48, 72
The factors of 72 are 24 and 72