# Divisibility - 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. Divisibility
Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero)
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 ??
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?
6. 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?
7. 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?
8. 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
9. Plums
In the bowl are plums. How many would be there if we can divide it equally among 8, 10 and 11 children?
10. 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?
11. Diofant 2
Is equation ? solvable on the set of integers Z?
12. 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)
13. Rectangles
How many rectangles with area 3032 cm2 whose sides is natural numbers are?
14. 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?
15. Group
Group of kids wanted to ride. When the children were divided into groups of 3 children 1 remain. When divided into groups of 4 children 1 remain. When divided into groups of 6 children 1 missed. After divided to groups of 5 children its OK. How many are t
16. Primes 2
Which prime numbers is number 2025 divisible?
17. 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.
18. Stacks
Annie has a total of \$ 702. The money must be divided into stacks so that each buyer has the same amounth of dollars. How many options she have?
19. Class
When Pythagoras asked how many students attend the school, said: "Half of the students studying mathematics, 1/4 music, seventh silent and there are three girls at school." How many students had Pythagoras at school?
20. 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.

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