Division + divisibility - practice problems - page 5 of 8
Number of problems found: 153
- Hens and pigs
Hens and pigs have 46 feet in total. At least how much can heads have? - Reminder and quotient
There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S and D:S are with the remainder of 1. - Reminder and quotient Numbers A = 135 and B = 315 are given. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1.
- Four poplars
Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be? - Bricks pyramid
How many 50 cm x 32 cm x 30 cm bricks are needed to build a 272 m x 272 m x 278 m pyramid? - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Middle finger
Jana counts on one hand, going finger by finger. She starts counting from her thumb through her index finger, middle finger, and ring finger up to her little finger, reaching the number 5. Then she immediately goes back to her ring finger (6), middle fing - Three-digit number
Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number. - Trees in alley
There are four trees in the alley between which the distances are 35 m, 15 m, and 95 m. 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? - Z7–I–5 MO 2018
At the Rose garden centre, one shop ordered a total of 120 roses in red and yellow, the second shop a total of 105 roses in red and white, and the third shop a total of 45 roses in yellow and white. The garden centre fulfilled the order, in such a way tha - Clock's gears
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? - 7 digit number If 3c54d10 is divisible by 330, what is the sum of c and d?
- Theater Seats Count
There are more than 320 seats in the theater and less than 330 seats, and there are 18 seats in each row. How many seats and seats are there in the theater? - Candy and boxes
We have some candy and empty boxes. When we put ten sweets in boxes, two candies and eight empty boxes will be left. When of eight, there will be six candies and three boxes left. How many candy and empty boxes are gone when we put nine sweets into a box? - Bus departure
Three lines depart from the bus station at 6-minute, 8-minute, and 12-minute intervals during the morning rush hour. Once in a while, they come out at the same time. How many times between 5:30 and 8:30 does this situation occur if they first go out toget - Z7-1-6 MO 2017
The water sprite Chaluha was pouring fog into various differently sized vessels, which he had carefully arranged on a shelf. When pouring, he proceeded gradually from one side, skipping no vessel. Into each vessel at least a decilitre of fog fits. If he w - Division with Remainder
What number did we divide by 55 if the ratio is 9.16 and the remainder is 0.04? - Remainder A is an arbitrary integer that gives remainder 1 in the division with 6. B is a random integer that provides the remainder with division by two. What makes remainder in a division by three products of numbers A x B?
- Groups
In the 6th class, there are 60 girls and 72 boys. We want to divide them into groups so that the number of girls and boys is the same. How many groups can you create? How many girls will be in the group? - Gardens colony
The garden's colony, with dimensions of 180 m and 300 m, is to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
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