# Prime numbers - problems

1. Dance group The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
2. The King The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?
3. Z9-I-4 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
4. No. of divisors How many different divisors has number ??
5. Numbers Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
6. Meadow 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?
7. Cherries Cherries in the bowl can be divided equally among 19 or 13 or 28 children. How many is the minimum cherries in the bowl?
8. Birthdate 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?
9. 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
10. Plums In the bowl are plums. How many would be there if we can divide it equally among 8, 10 and 11 children?
11. Plumber 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?
12. Diofant 2 Is equation ? solvable on the set of integers Z?
13. Seedcake Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
14. 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)
15. LCM What is the least common multiple of 36, 44, 21?
16. Rectangles How many rectangles with area 3032 cm2 whose sides is natural numbers are?
17. Game room Winner can took win in three types of jettons with value 3, 30 and 100 dollars. What is minimal value of win payable in this values of jettons?
18. Sugar - cuboid Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i
19. Primes 2 Which prime numbers is number 2025 divisible?
20. Amazing number An amazing number is name for such 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 amazing numbers.

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