Prime numbers - problems
The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
- Minimum surface
Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
- Diofant equation
250x + 120y = 5640
- Cube root
Find cube root of 18
- Counting number
What is the smallest counting number divisible by 2,5,7,8 and 15?
- Sum of two primes
Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
- 7 digit number
If 3c54d10 is divisible by 330, what is the sum of c and d?
Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
- No. of divisors
How many different divisors has number ??
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
On the meadow grazing horses, cows and sheep, together 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 equall. How many horses, cows and sheep are on the meadow together?
Cherries in the bowl can be divided equally among 8 or 10 or 11 children. How many is the minimum cherries in the bowl?
Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?
- Mr. Zucchini
Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. Content area of the garden filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and
In the bowl are plums. How many would be there if we can divide it equally among 10, 12 and 14 children?
- Diofant 2
Is equation ? solvable on the set of integers Z?
Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
- Diofant equation
In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
What is the least common multiple of 10, 30, 48?