fill (up) a vacancy

Numbers divisible by 1 and 15 must be divisible by (1, 3,5). [Write down all possibilities]

2. Choose four different numbers from 0, 2, 3, 7 and 8 to form a four-digit number with factors of 2, 3 and 5, of which the largest is (8730) and the smallest is (2370). Solution: There are two possibilities: 0, 3, 7, 8 and 0, 2, 3, 7.

3. The sum of six consecutive even numbers is 2 10, and these six even numbers are (30, 32, 34, 36, 38, 40).

4. Of the six numbers15, 19, 27, 35, 5 1 and 9 1, the only number is (19), because (only 19 is a prime number, and.

The product of two prime numbers is 46, and the sum of these two prime numbers is (25).

Solution: Because 46 is an even number, it must be the product of an odd prime number and an even prime number, while the even prime number is only 2, and the other prime number is 46÷2=23, so the sum of 2 and 23 is 25.

6, 1992 The sum of all prime factors is (88).

Solution: 1992 = 222383, so the sum of all prime factors of 1992 is 2+2+2+3+83 = 92.

7. There are two numbers that are both composite numbers and prime numbers, and their least common multiple is 90. These two numbers are (9 and 10).

8. The greatest common factor of several numbers is the (cause) number of the least common multiple, and the least common multiple of several numbers is the (multiple) number of the greatest common factor.

9. All (factorial) numbers of (greatest common factor) numbers of several numbers are common factors of these numbers; All (least common multiple) numbers of several numbers are common multiples of these numbers.

10, a, B A÷B=C are all non-zero natural numbers, and a b = c, then the minimum common multiple of a and b is (a), the maximum common factor is (b), c is the factor of (a), and a is the (multiple) number of b.

1 1, number A = 2× 3× 5× a, number b = 2× 3× 7× a. If the greatest common factor of a and b is 30, then a should be (5); If the least common multiple of A and B is 630, then A should be (3).

12, natural number A = B- 1, both a and b are non-zero natural numbers, the greatest common factor of a and b is (1), and the smallest common multiple is (AB).

Two application problems 13, length 180 cm, width 45 cm, height 18 cm, how many cubes of the same size can be sawed at least?

Solution: The greatest common factor of 180,45 and18 is 9. When the side length of the sawed cube is 9 cm, the number of sawed cubes is the least, which is (180 ÷ 9) × (45 ÷ 9 )× (65433).

14. How many cuboid blocks does it take to build a cube with cuboid blocks of 9 cm long, 6 cm wide and 7 cm high?

Solution: The minimum common multiple of 9, 6 and 7 is 126, that is, the minimum side length of the stacked cube is 126 cm, at least (126 ÷ 9) × (126 ÷ 6 )× (/kloc).

15, students train in line. If there are 8 people in each row, there are 6 people in the last row. If there are 10 people in each row, there are 4 people missing in the last row. What is the minimum number of people participating in queue training?

Solution: According to the meaning of the question, the number of students divided by 8 plus 6 and divided by 10 is also 6, so it is the least common multiple of 8 and 10 plus 40 plus 6, and the minimum number of students is 40+6 = 46.

16, Xiaohong, Xiaolan, Xiaogang and Xiaohua, their ages are just one year older than Fang, and the product of their ages is 5040. So, how old are Xiaohong, Xiaolan, Xiaogang and Xiaohua?

Solution: 5040 = 2× 2× 2× 3× 5× 7 = 7× (2× 2× 2 )× (3× 3 )× (2× 5), which are 7, 8, 9 and 10 years old respectively.

Three. Complete the following squares and rectangles.

17. Write the formula of the side area of a cuboid: the side area of a cuboid = () × ().

18. If the side length of the cube is expanded to 3 times, the surface area and volume of the cube will be expanded to 9 times and 27 times respectively.

19. It takes at least eight small cubes to make a larger cube. At this time, the surface area of the larger cube is ((2× 2× 6) ÷ (1× 1× 6) of the original surface area of each small cube.

20. A cuboid with a square bottom, 2 decimeters high, happens to be square when the side is unfolded. How many cubic decimeters is the volume of this cuboid?

Solution: The length and width are both 2 ÷ 4 = 0.5 decimeter, and the volume is 0.5× 0.5× 2 = 0.5 cubic decimeter.

2 1. A classroom is 8 meters long, 6 meters wide and 4 meters high. There are 32 students in the classroom. How much space does each student occupy on average?

Solution: 8× 6× 4 = 192 cubic meters, 192 ÷ 32 = 6 cubic meters.

22. A wooden box without a lid, measured from the outside, is 1 0cm long, 8cm wide, 5cm high, and its thickness is1cm. What is the volume of this wooden box?

Solution: length 10- 1× 2 = 8cm, width 8- 1× 2 = 6cm, height 5- 1 = 4cm, volume 8× 6× 4 = 192cm.

23. Cut a cuboid whose length, width and height are 5 decimeters, 3 decimeters and 2 decimeters respectively into two small cuboids, and the maximum sum of the surface areas of these two small cuboids is () square decimeters.

Solution: The surface area of the original cuboid is 5× 3× 2+5× 2× 2+3× 2× 2 = 62 square decimeters. After being cut into two small cuboids, the surface area will increase by 5× 3× 2 = 30 square decimeter at most, and the maximum sum of the surface areas of these two small cuboids is 62+30 = 92 square decimeter.

24. There is a cuboid. If its length is reduced by 2 decimeters, it will become a cube and its surface area will be reduced by 48 square decimeters. Find the volume of this cuboid.

Solution: the cross section is square, that is, the width and height are equal. The width and height of a cuboid are 48 ÷ 4 ÷ 2 = 6 decimeters, the length is 6+2 = 8 decimeters, and the volume is 8× 6× 6 = 288 cubic decimeters.

25. How many cubes can you get by cutting a 6 cm long cube into a 2 cm long cube? How many square centimeters has the surface area increased?

Solution: Cut into (6 ÷ 2) × (6 ÷ 2) × (6 ÷ 2) = 27 cubes, and the surface area increased by 6 × 6× 4× 3 = 432 square centimeters.

26. Two identical cubes are combined into a cuboid. The surface area of this cuboid is 40 square centimeters. How many square centimeters is the surface area of each small cube?

Solution: One side of a small cube is 40 ÷ (5× 2) = 4cm2, and the surface area of each small cube is 4x6 = 24cm2.

27. A rectangular glass container with 6 liters of water. At this time, the water level is 15 cm. Put an apple in water, and the water level in the container is 16.5 cm. Please work out the size of this apple.

Solution: 6 liters = 6000 ml, the bottom area is 6000 ÷ 15 = 400 square centimeters, and the volume of apples is 400× (16.5-15) = 600 cubic centimeters.

4. The significance and nature of music score:

The decimal unit of 28 and 2 is (), which has (37) such decimal units, and (23) such decimal units are equal to the minimum composite number.

29. There are a true score, a false score and a score with a denominator of 7, and their sizes are only one fractional unit. These three scores are (,1).

30. When the numeralization of a fraction is original and the denominator is original, the value of this fraction will be (tripled).

3 1, a car travels 9 kilometers in 6 minutes, it takes () minutes to travel 1 km, and 1 min can travel (1.5) km.

32, < < 1, the natural number that can be filled in □ is (). [Write down all possibilities]

Solution: