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Reminder and quotient
There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1,
Plumber
The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
Granddaughter 2789
Grandma and her granddaughter Barunka have a birthday on the same day. During six consecutive birthday celebrations, Grandma's age was always divisible by Barunka's age. How many birthdays did Grandma celebrate at the last of these six celebrations? Grand
Decompose 3076
Decompose into primes and find the greatest divisor of the pair of numbers D (84.70).
On Children's
On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.
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.
The classroom
The classroom is 9 meters long. The width of the classroom is smaller and can be passed in equally long steps of 55 CM or 70 CM. Determine the width of the classroom.
Decompose
Decompose into primes and find the smallest common multiple n of (16,20) and the largest common divisor D of the pair of numbers (140,100)
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, the smallest commo
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.
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?
Lcm and hcf
If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a = …
Diofant equation
In the set of integers (Z) solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
Seedcake
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
Diofant 2
Is equation 70x +52y = 34 solvable on the set of integers Z?
Hectares
The tractor plows the first day of 4.5 ha, the second day 6.3 ha, and the third day of 5.4 ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is i
