Fill in the three boxes of the six digit number 3, 2, 1 so that the number can be divided by 15. The smallest of the six digits is______ ．

3 + 2 + 1 = 6, 6 is a multiple of 3, in order to make the composition of the six digit minimum, all three must be filled with 0; so the answer is: 302010

173__ It's a four digit number. The math teacher said, "I'll fill in three numbers in the box one after the other, and the three four digit numbers will come out in turn (see the supplement to the question)
Q: what is the sum of the three numbers filled in by the math teacher?

The three numbers filled in are 7, 8 and 9 respectively, and the sum of the three numbers is 24

(7) Fill in the appropriate number in the box of 3 ×× 2 ×, so that the four digit can be divided by 15. The largest of the four digits is ()

To be divisible by 15 is to be divisible by 3 and 5 at the same time
So one bit is 0 or 5
Let 100 be X
Then when the bit is 0, 3 + X + 2 + 0 can be divided by 3, and the maximum x is 7
This is 3720
When the number of bits is 5, 3 + X + 2 + 5 can be divided by 3, and the maximum x is 8
Now the number is 3825
So the maximum is 3825

537 is a four digit number. The math teacher said, "I fill in three numbers in this number, and the three four digit numbers can be divided by 9, 11 and 6 in turn
What is the maximum sum of the three numbers filled in by the math teacher?

537: a number divisible by 9
The number divisible by 11 is 5379
The numbers divisible by 6 are 5376 and 5370
So the three numbers could be 3, 9, 6 and 3, 9, 0
Of course, the biggest sum of the three numbers is 3 + 9 + 6 = 18

What are the characteristics of numbers divisible by 11?
Not after 35

Sum of numbers on odd digits
And
Sum of numbers on even digits
The difference is a multiple of 11

Four consecutive natural numbers can be divided by 7, 9, 11 and 13 to find the smallest group of numbers

The original problem can be converted into: a natural number, can be divided by 13, divided by 11 odd 1, divided by 9 odd 2, divided by 7 odd 3, to find the minimum value of this number. Then according to the Chinese remainder theorem, first of all, find out four unknowns which can be divided by any three numbers and satisfy the remainder of the fourth

How many natural numbers are less than 500 and divisible by 5 and 7 at the same time?

Three continuous natural numbers, of which the minimum can be divided by 17, the middle by 14, and the maximum by 11. What is the minimum number among the three numbers?

Let the number in the middle be x, then x divided by 14, the remainder is x divided by 17, the remainder is 1x divided by 11, and the remainder is 10. Then I remember a Han Xin Dianbing said this kind of question, you should know it yourself? Well, the following website is asked how to calculate Han Xin Dianbing, copy the website for you, OK, and study the algorithm for you, then

How many natural numbers from 1 to 1000 are not divisible by 3 and 2

The multiple of 2 is 500, 333 of 3, and 166 of 3 and 2, so it's 1000-333-500 + 166 = 333

Among the natural numbers from 1 to 10000, there are () numbers that cannot be divisible by 31 and 13 at the same time
Divide 50 into the sum of 10 prime numbers, and ask the largest prime number to be as large as possible. Then, what is the maximum index?

1.
The least common multiple of 31 and 13: 31 × 13 = 403
10000 / 403 = more than 24 328
That is, 24 can be divided by 31 and 13 at the same time
Then there are 10000-24 = 9976 that cannot be divisible by 31 and 13 at the same time
two
The smallest prime number is 2
9×2=18
50-18 = 32 is not prime
8×2+3=19
50-19=31
So the maximum prime number is 31

Fill in the three boxes of the six digit number 3, 2, 1 so that the number can be divided by 15. The smallest of the six digits is______ ．