Prime numbers - problems

  1. Hectares
    tractor_8 The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor
  2. MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  3. Prime number
    prime_2 Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
  4. Dance ensemble
    dancers_1 The dance ensemble took the stage in pairs. During dancing, the dancers gradually formed groups of four, six and nine. How many dancers have an ensemble?
  5. Clock's gears
    orloj In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position?
  6. Inverted nine
    In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
  7. Z9-I-4
    numbers_30 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
  8. No. of divisors
    triangle_div How many different divisors has number ??
  9. Numbers
    ten Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
  10. Meadow
    ovce-miestami-baran 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?
  11. Cherries
    visne Cherries in the bowl can be divided equally among 8 or 10 or 11 children. How many is the minimum cherries in the bowl?
  12. Birthdate
    lizatka 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?
  13. Mr. Zucchini
    cuketa 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
  14. Plums
    svestka In the bowl are plums. How many would be there if we can divide it equally among 10, 12 and 14 children?
  15. Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  16. Plumber
    klempir 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?
  17. Seedcake
    pletenky Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
  18. Diofant equation
    diofantos 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)
  19. LCM
    calc_icon What is the least common multiple of 36, 44, 21?
  20. Rectangles
    rectangles How many rectangles with area 3002 cm2 whose sides is natural numbers are?

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