Prime numbers + divisibility - practice problems - page 4 of 11
Number of problems found: 212
- Banknotes
How many different ways can the cashier pay out € 310 if he uses only 50 and 20 euro banknotes? Find all solutions. - 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? - Three-digit 8002
Find the largest three-digit number that gives the remainder 1 when divided by three, gives the remainder 2 when divided by four, gives the remainder 3 when divided by five, and gives the remainder 4 when divided by six. - 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
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. - The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in - Six-digit primes
Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they? - The florist
The florist had 200 roses in the morning. During the day, more than half sold it. The remaining roses will tie to the bouquet. One always remains if a bouquet of 3, 4, 5, or 6 roses is bound. How many roses from the morning shipment were sold? - Chocolate
I have a box of chocolate - white, milk, and dark. The ratio of white to milk with dark is 3:4. The ratio of white and milk to dark is 17:4. Calculate the ratio between white, milk, and dark chocolate.
- 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 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid? - 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 equal and 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? - Exercisers
How many exercisers are in the gym (minimum number) if there is one left after ordering into three, four, and five steps? - Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of - Dance ensemble
The dance ensemble took the stage in pairs. During dancing, the dancers gradually formed groups of four, six, and nine. How many dancers have an ensemble? - 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?
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