1. If a number has only two factors, such a number is called a prime number. (e.g. 2, 3, 5)

② Write five complex numbers: (4), (8), (9), (6) and (10).

(1) is neither a prime number nor a composite number.

④ The smallest prime number is (2).

⑤ Two adjacent prime numbers are (2) and (3) respectively, and two adjacent composite numbers are (8) and (9) respectively.

6. The number that is both even and prime is (2).

⑦ Fill in the appropriate prime numbers in the following ().

10=( 3 )+( 7 )=( 2 )+( 5 )+( 3 )

16=( 13 )+( 3 )

20=( 13 )+( 7 )=( 1 1 )+( 2 )+( 7 )=( 17 )+( 3 )

Second, judge.

① A composite number has at least three factors. (correct)

② The product of two prime numbers is a prime number. (correct)

③ If the natural number C is a prime number, then C has only two factors. (correct)

4. The composite number must be even. (error)

There are 84 tons of goods in the warehouse, and there are three trucks with different loads. Which truck can deliver goods many times, just enough to finish loading?

(1), 2-ton truck; (2) A truck with a deadweight of 3 tons; (3) A truck with a deadweight of 5 tons.

(Select) (Select) (Don't select)

4. Which two prime numbers are multiplied by the following figures respectively?

15=( 3 )×( 5 ) 39=( 3 )×( 13 )

33=( 1 1 )×( 3 ) 46=( 2 )×( 23 )

5. There is a four-digit number, the smallest prime number is in the tenth place and the smallest composite number is in the hundredth place. If this number has factors 2, 3 and 5 at the same time, then the maximum value of this four-digit number is (9420).

Solution: Let the thousand digits be a and the unit digits be b, because the minimum prime number is 2 and the minimum composite number is 4, then:

Four digits = 1000a+400+20+b

Because this number has factors 2, 3 and 5 at the same time. So this number can be divisible by 2, 3 and 5, so:

①( 1000 a+420+b)÷2 = 500 a+2 10+？ ×b

Analysis 1: 1000a÷2=500a, and the result is an integer, then the value range of a is1~ 9; b÷2=？ ×b, b should be an even number, which can be 0, 2, 4, 6, 8. If this number is the largest four digits that meet this condition, A takes 9 and B takes 8. (9428)

②( 1000 a+420+b)÷3 = 1000/3×a+ 140+？ ×b

Analysis 2:1000a ÷ 3 =1000/3× a, and the result is an integer, then the value range of a is 3, 6 and 9; b÷3=？ ×b, b should be a multiple of 3, which can be 0, 3, 6, 9. If this number is the largest four digits that meet this condition, A takes 9 and B takes 9. But according to the analysis, 1, b is even, so b only takes 6 (maximum). (9426)

③( 1000 a+420+b)÷5 = 200 a+84+ 1/5×b

Analysis 3: 1000a÷5=200a, and the result is an integer, then the value range of a is1~ 9; B÷5= 1/5×b, and b should be a multiple of 5, which can be 0 or 5. If this number is the largest four digits that meet this condition, A takes 9 and B takes 5. However, from analysis I and analysis II, it can be seen that B is an even number and a multiple of 3, so B only takes 0 (satisfying the conditions). (9420)

To sum up, then the maximum value of this four-digit number is 9420.

A: The maximum value of this four-digit number is 9420.

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