Divisibility - math problems
Number of problems found: 213
- All pairs
Determine 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.
- 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
- Tractor wheels
The front wheel of the tractor has a circumference of 18 dm and the rear 60 dm. We will make a red mark on the lowest point of both wheels. The tractor then starts. At what distance from the start will both marks appear identically at the bottom again?
Three buses follow the same circular route. The first driver is the slowest because he has many stops, and it takes him 90 minutes to cross the route. The second driver will pass the circuit in 1 hour. The third driver has the fewest stops, and the circui
From two sticks 240 cm and 210 cm long, it is necessary to cut the longest possible pegs for flowers so that no residues remain. How many pegs will it be?
- Sum of odd numbers
Find the sum of all odd integers from 13 to 781.
- Divisible by nine
How many three-digit natural numbers in total are divisible without a remainder by the number 9?
- How many
How many numbers are less than 222 with a digit sum is 8?
- Drawing from a hat
When drawing numbers from a hat from 1 to 35, we select random given numbers. What is the probability that the drawn numbers will be divisible by 8 and 2?
- How many 4
How many four-digit numbers that are divisible by ten can be created from the numbers 3, 5, 7, 8, 9, 0 such no digits repeats?
- The sum
The sum of five consecutive odd numbers is 75. Find out the sum of the second and fourth of them.
Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order.
- Columns of two and three
When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class?
- Tram stop
The blue tram stops every 12 minutes, the red one 8 minutes. At 8 o'clock they left the stop together. How many times do they meet at a stop before 11 am?
- 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, there will always be one rose lef
- 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.
The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 of these tiles have so that no tile remains?
- An example
An example is playfully for grade 6 from Math and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: A cuboid was made from a block of 16x18x48 mm of modeline. What will be the edge of t
- Children's home
The children's home received a gift to Nicholas of 54 oranges, 81 chocolate figurines, and 135 apples. Every child received the same gift and nothing was left. a) How many packages could be prepared? b) what did the children find in the package?
How many are three-digit natural numbers divisible by 25?