# Divisibility - problems

- Odd/even number

Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time. Prove. .. - Year 2018

The product of the three positive numbers is 2018. What are the numbers? - Trees in alley

There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them? - MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Prime number

Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number? - Divisibility

Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero) - 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 - No. of divisors

How many different divisors has number ?? - 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? - Cherries

Cherries in the bowl can be divided equally among 8 or 10 or 11 children. How many is the minimum cherries in the bowl? - 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? - 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 - Plums

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

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? - 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) - Rectangles

How many rectangles with area 3002 cm^{2}whose sides is natural numbers are? - 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? - 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 - 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.

Do you have interesting mathematical problem that you can't solve it? Enter it and we can try to solve it.