Prime numbers + divisibility - practice problems - page 10 of 11
Number of problems found: 208
- Unknown integer
Find the smallest integer: Divided by 2, the remainder is 1. divided by 3. The remainder is 2. divided by 4. The remainder is 3. Divided by eight, the remainder is 7. Divided by 9, the remainder is 8. - 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 - Tiles
Hall has dimensions 250 × 200 dm. What is the largest size of square tiles that can be entire hall tiled, and how many do we need them?
- 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 - 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.
- 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? - Package
The package has no more than 66 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left to remain. On the one blouse consumes 1.3 m of cloth and on one dress 5 m. Determine the amount of the cloth in the package. - Stacks
Annie has a total of $ 702. The money must be divided into stacks so that each buyer has the same amount of dollars. How many options she has? - 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. - Plums
In the bowl are plums. How many would be there if we could divide it equally among 8, 10, and 11 children? - Game room
The winner can take the win in three types of jettons with value 3, 30, and 100 dollars. What is the minimum value of win payable in these values of jettons? - Chebyshev formula
To estimate the number of primes less than x Chebyshev formula is used: Pi(x) = 1.11 (x)/(ln x). Estimate the number of primes less than 30300537. - No. of divisors
How many different divisors have number 13 4 * 2 4?
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