Natural numbers + divisibility - practice problems
Number of problems found: 280
- Same remainder
Find the greatest number that will divide 43, 91, and 183 so as to leave the same the remainder in each case. - Relay teams
There are 159 students to be grouped into relay teams. Each team should have the same number of students. Can each team have 3,5 or 6 students? Explain. - A number 8
A number K is such that when it is divided by 27, 30, or 45, the remainder is 3. Find the smallest possible value of K - Unknown number 35
I am a number between 121 and 149. I can be divided by both 3 and 5. What number am I?
- Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around the 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth - Intelligence test
Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus seven questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions, and Risho to a fifth plus 25 questions. After the tes - Significant 9321
Only herbs with 5 and 7 leaves grow in the Old Forest. When the boar Vavřínec collects raw materials for herbal liquor, it always tears off the whole herb and puts it in a basket. What is the most significant number of letters he will ever manage to have - Composition 83241
You have to create as many identical candy boxes as possible from 280 orris, 252 nougat, and 420 marzipan candies. At the same time, you must not have any candy left or missing. What will be the composition of one box of chocolates, and how many candies w - Symmetry
Eva loves symmetry in shapes and numbers. Yesterday she invented an entirely new kind of symmetry - divisible symmetry. She wrote all five-digit numbers with different digits with the following property: The first digit is divisible by 1, the second by 2,
- Rectangular 54871
The arranger has at his disposal a certain number of colored targets, from which he wants to create a rectangular pattern of a flower bed. If he puts 4,5,6,8,9, or 10 targets in one row, he always has three extra targets. How many targets does it have? De - The florist
A consignment of 200 roses arrived at the florist in the morning. She sold more than half of them during the day. She wants to tie bouquets of the remaining roses. If she ties a bouquet of three, four, five, or six roses, one rose will always be left. Det - 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 equal and maximum. How many trees will they put in, and what will be the distance between them? - Different 7909
Kryštof sells 10 bells at different prices: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 euros. He needs to pack all the bells into 3 boxes so that the price of the bells in each box is the same. How many ways can he do this? A)1 b)2 c)3 d)4 e)cannot be divided in this - Reminder and quotient
There are given numbers A = 135, B = 315. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1.
- Tissues
The store got three kinds of tissues - 132 children, 156 women, and 204 men. Tissues for each species were packed into boxes after the number of pieces was the same for all three types (and greatest). Determine the number if you know that every box has mo - Divisible 79464
The teacher wrote a number less than 50,000 on the board. The first student said: This number is divisible by 2 The second student said: This number is divisible by 3 And so on, down to the last one who claimed it was divisible by 13. Two in a row lied. W - Summer camp
Some boys or girls signed up for the summer camp, which has a maximum capacity of 200 children. The main leader noticed that during the evening start, he could arrange the participants exactly in the twelve-step, sixteen-step, or eighteen-step, and no one - Prepared 66494
Benches were prepared around the fire. When seven tourists sit on them, one tourist will sit alone on the last bench. When six of them all sat down, one had to stand. How many tourists were at the campfire if we know there were less than 100, and how many - Simultaneously 7748
The monitor screen is blank. Four new wheels appear on the screen every seven seconds when the beep sounds. On the contrary, three wheels disappear from the screen every eleven seconds. If both actions should take place simultaneously, the number of circl
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