# Greatest common divisor (GCD) + divisibility - practice problems

#### Number of problems found: 48

- Determine 70224

Determine the number by which all these numbers, 22, 18, 25, 15, 35, and 10, are divisible without remainder. The number is greater than 1. - Two-digit 68654

List all compound positive two-digit numbers whose greatest common divisor with the number 51 is the number 17. - Lcm = 22 + gcd

The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers. - Coloured numbers

Mussel wrote four different natural numbers with colored markers: red, blue, green, and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div - Pegs

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? - Children's home

The children's home received a gift from 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? - Intervals 12201

Trams of five lines run at intervals of 5, 8, 10, 12, and 15 minutes. At noon they left the station at the same time. What time will they meet again? How many times will each tram pass the stop during that time? - Common divisors

Find all common divisors of numbers 30 and 45. - Length of a string

What are the smallest length of a string that we can cut into 18 equal parts and even 27 equal parts (in decimeters)? - Seven numbers

Write seven 4-digit numbers divisible by three and at the same time by 4. - Matemakak 9432

The cookbook by Matěj Matemakak said: The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest c - Determine 8611

Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product. - 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. - 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? - 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. - Three friends

Three friends had balls in a ratio of 2:7:4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together. - Orienteering 6301

Twenty-six girls and 39 boys took part in the orienteering race. Create as many of the same teams as possible so that no competitor is left. How many boys and how many girls are on the team? - Dimensions 6201

Mr. John's plot of land has dimensions of 252 dm and 28 m. How far apart must he place the fence posts so they are the same distance on both sides? How many will he need to fence the entire property?

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