Natural numbers + divisibility - practice problems - page 13 of 14
Number of problems found: 280
- Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - All pairs
Find all pairs (m, n) of natural numbers for which is true: m s (n) = n s (m) = 70, where s(a) denotes the digit sum of the natural number a. - 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? - Three buses
Three public transport buses depart together from the bus station in the morning. The first bus returns to the station after 18 minutes, the second after 12 minutes, and a third after 24 minutes. How long will again together at the station? Please express
- 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 - Cuboid
The volume of the cuboid is 245 cm³. Each cuboid edge length can be expressed by an integer greater than 1 cm. What is the surface area of the cuboid? - Integer cube
The length of the cube edge is an integer. Its volume is in cm3, a five-digit number divisible by 1331. What is the length of the edge of this cube? - Blades
1st blade 2,5 m, 2nd blade. .1.75 m. How many can the same long pieces of these two blades do the biggest? How long is one piece? - Air draft
The number 1,2,3,4,5 are written on five tickets on the table. Air draft randomly shuffled the tickets and composed a 5-digit number from them. What is the probability that he passed: and the largest possible number b, the smallest possible number c, a nu
- Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Tram stop
The blue tram stops every 12 minutes, the red one for 8 minutes. At 8 o'clock, they left the stop together. How many times do they meet at a stop before 11 AM? - Three numbers
We have three different non-zero digits. We will create all three digits numbers from them to use all three figures in each. We add all the made numbers and get the sum of 1554. What were the numbers? - Divisible 6615
How many 3-digit numbers can be composed of the digit 1,3,5,7,9 if the digits are not allowed to be repeated in the number notation? How many of them are divisible by five? - Probability 17013
What is the probability that a randomly written two-digit number from number 20 to number 99 will be divisible by 11, the power of number 3, or a prime number?
- Notation 7014
There is no 0 in the decimal notation in natural numbers, and there are even numbers or odd numbers, each at least once. Find the number of all k-digit natural numbers. - Three digits number
From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there? - Two-digit 3456
Write all the two-digit numbers that can be composed of the digit 7,8,9 without repeating the digits. Which ones are divisible b) two, c) three d) six? - Expression 4451
Find the largest natural number d that has that property for any natural number the number n is the value of the expression V (n) = n ^ 4 + 11n²−12 is divisible by d. - Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
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