Prime numbers - high school - practice problems - page 2 of 3
Number of problems found: 47
- Measured 4046
Peter cut the two bars into equal parts but made them as large as possible. One rod measured 42 cm, the other 63 cm. How many cuts did he have to make? - Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - Remembered 2766
Aunt bought 6 identical mugs and one coffee pot. She paid €60 in total. A teapot was more expensive than one mug but cheaper than two mugs. Auntie remembered that all the prices were in whole euros. How much € was one mug, and how much was a kettle? - Meadow
On the meadow grazing horses, cows, and sheep, together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equal. How many horses, cows, and sheep are on the meadow togethe
- Amazing number
An amazing number is a name for such an even number, the decomposition product of prime numbers has exactly three, not necessarily different factors, and the sum of all its divisors is equal to twice that number. Find all the amazing numbers. - Grandson and granddad
Grandson with grandpa, they counted how many years have together. Their product is 365. How many years is the sum of their years? - Numbers
Write the smallest three-digit number in divisions 5 and 7, and gives the rest 2. - Two months
Mars has two months, Phobos and Deimos. Phobos orbit around Mars in 7 hours 39 minutes, and Deimos in 30 hours 14 minutes. How long will the relative positions of the three celestial bodies repeat? - Four-digit number
Find a four-digit number, which quadrupled written backward is the same number.
- 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? - Mushrooms from the forest
Magda and Tereza go to pick mushrooms. Found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms were found, Magda? - Combinations
How many different combinations of two-digit number divisible by four arises from the digits 3, 5, and 7? - Unknown number
An unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference between the first and second prime numbers is half the difference between the third and second prime num - 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
- 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 - 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. - Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles. - 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?
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