School year

At the beginning of the school year, 396 notebooks and 252 textbooks are ready to be distributed in the classroom. All pupils receive the same number of notebooks and the same amount of textbooks. How many pupils are there in the class if you know that there are more than 30 and less than 50?

Correct result:

n =  36

Solution:

$396=2^2 \cdot 3^2 \cdot 11 \ \\ 252=2^2 \cdot 3^2 \cdot 7 \ \\ \text{GCD}(396, 252)=2^2 \cdot 3^2=36 \ \\ \ \\ n=GCD(396,252)=36 \ \\ s=396/n=396/36=11 \ \\ u=252/n=252/36=7 \ \\ \ \\ 30<n<50 \ \\ \ \\ n=36$

Try another example

Showing 0 comments:

Next similar math problems:

• Write decimals
  Write in the decimal system the short and advanced form of these numbers: a) four thousand seventy-nine b) five hundred and one thousand six hundred and ten c) nine million twenty-six
• Lcm simple
  Find least common multiple of this two numbers: 140 175.
• Lcm of three numbers
  What is the Lcm of 120 15 and 5
• Counting number
  What is the smallest counting number divisible by 2,5,7,8 and 15?
• Biketrial
  Kamil was biketrial. Before hill he set the forward gear with 42 teeth and the back with 35 teeth. After how many exercises (rotation) of the front wheel both wheels reach the same position?
• Apples 2
  How many minimum apples are in the cart, if possible is completely divided into packages of 6, 14 and 21 apples?
• School
  Headteacher think whether the distribution of pupils in race in groups of 4,5,6,9 or 10. How many pupils must have at least school at possible options?
• Balls groups
  Karel pulled the balls out of his pocket and divide it into the groups. He could divide them in four, six or seven, and no ball ever left. How little could be a ball?
• LCM of two number
  Find the smallest multiple of 63 and 147
• 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?
• Buildings
  The school stands 110 m from the church, which is 100 m beyond the town hall. Which building are closer to the church and how many times?
• Chairs
  In the two dining rooms in the recreational building, there are equally arranged chairs around the tables. A maximum of 78 people can dine in the first dining room and 54 people in the second. How many chairs can be around one table?
• Lamps on playground
  The playground has the shape of a rectangle 36 x 50m. After how many meters will he place the lamps on his lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps?
• The port
  Four ships Berthed in the port. Together sail from a port. The first ship will return to port every two weeks, second ship after 4 weeks, third after 8 weeks and fourth ship after 12 weeks. After how many weeks all the boats gather at the port?
• Cents no more
  Janko bought pencils for 35 cents each. Neither he nor the salesperson had small coins just a whole € 1 coin. At least how many pencils had to buy to pay for the whole euros?
• Four families
  Four families were on a joint trip. In the first family, there were three siblings, namely Alica, Betka and Cyril. In the second family were four siblings, namely David, Erik, Filip and Gabika. In the third family, there were two siblings, namely Hugo and
• Gears
  The gearing fits wheel with 20 teeth to the wheel with 36 teeth. Before starting the machine is stained tooth smaller wheels in the designated space between the teeth of the larger wheels. How many times after starting the machine wheels turning that stai