Prime numbers - practice for 13 year olds - page 8 of 9
Number of problems found: 165
- Plumber
The plumber had to cut the metal strip with dimensions of 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it? - Spartakiada
Practitioners lined up in rectangles with a row with four, five, or six exercisers, one always missing an entire rectangle. How many exercisers were on the field, if they have estimated not been more than 100? - Around the flowerbed
Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses are found in every corner of the flowerbed and consumed as little as possible. a) At what distance are planted roses? b) How many rose - Nuts
How many must we have at least nuts if we can equally divide it to 10 children, 12 children, or 15 children and any nuts left?
- Birthdate
Jane brought 30 lollipops and 24 chewing gum for their friends on her birthday. How many friends does she have if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friends? - Sports games
Pupils of the same school participated in district sports games. When dividing into teams found that in the case of the creative teams with four pupils remaining one pupil, in the case of five-member teams with remaining two pupils, and in the case of six - Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm, is sketched a snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over the snowman is the same as under it, 3. diameters of all circles - Racing track
On the racing track circling three cars. The first pass one circuit for 8 seconds, the second for 20 seconds, and a third for 8 seconds. a) Calculate the number of seconds since starting to catch all three cars together for the first time again across the - Snowman
In a circle with a diameter of 40 cm are drawn three circles (as a snowman) where: its diameters are integers, each larger circle diameter is 2 cm larger than the diameter of the previous circle. Determine snowman height if we wish for the highest snowman
- Sugar - cuboid
Pablo received from his master a cuboid composed of identical sugar cubes with a count between 1000 and 2000. The Pejko eat sugar cubes in layers. On the first day, eat one layer from the front. On the second day, one layer from the right, and on the thir - Decomposition
Make decomposition using prime numbers of number 155. The result write as prime factors (all, even multiple) - Divisors
The sum of all divisors unknown odd number is 2112. Determine the sum of all divisors of a number that is twice unknown numbers. - Segments
Line segments 69 cm and 3.7 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - Bouquet
The gardener tied a bouquet of flowers for eight, and none was left. Then he found that he could tie a bouquet of 6 flowers and also none was left. How many have gardener flowers (minimum and maximum) if they had between 50 and 100 flowers?
- TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the actual program's minutes. Determine how many minutes of the program are shown in that one hour. - Count of roots
How many solutions have equation x. y = 7757 with two unknowns on the set of natural numbers? - Divisibility
Determine the smallest integer which divided 11 gives remainder 4. When divided, 15 gives remainder 10 and when divided by 19 gives remainder 16. - Trams
Two trams started at the same time from the same place. One tram journey takes 30 minutes, and the second 45 minutes to its final stop. How long will the trams meet again? - Lines
Five bus lines run at intervals 3, 6, 9, 12, 15 minutes. In the morning, it suddenly starts at 4:00. After how many minutes do the bus lines meet again?
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