A teacher has 30 pens and 45 pencils that he wants to give to his students. If each student were to receive the same number of pens and the same numbers of pencils with none left over, then what is the maximum number of students that this teacher could have?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
no solutions indeed. just mental math
2 pen for and 3 pencil for every child
basically, 30/45 = 2/3 => each student will have 2 pens and 3 pencils
HCF of 30 and 45 is 15
Am I the only one to realize that pencils can easily be broken in half? 1.5 pencils and a pen to each student results in 30 students able to take notes. There's little chance this elementary school teacher has only 15 pupils.
Log in to reply
Me too...entered 30 and got wrong. Its not told anywhere that we need to distribute all. So just thought 30 pencils and 30 pens among 30 students.
I think ur right
how to slove the problem
1.5 pencils mean 1 pencil and it's half mean a broken pencil
the question didn't imply that the teacher has to give away "all" his pens and pencils.. so he could have given away 30 pairs of pens and pencils for each student, having 15 pencils left with him.. then the maximum number of student he could have was to be 30.
Log in to reply
It is written "with none left over"
Even that the question didn't imply that, the maximum number would be 45. He could give 1 pencil to each student and 0 pens. But as it is written "with none left over" the maximum is the gcd(30,45)=15.
the question say with none left over!!!
The problem can be very easily solved using the concept of greatest common divisor,but let's look at it in other way.(You'll find out that this 'other way' is just another way of using the same concept of GCD. Let n be the no. of students,x be the no. of pens and y be the no. of pencils that each of them receive. Then for no left overs,we must have, n(x+y)=45+30=75 Also, nx=30 and ny=45. Thus,x/y=30/45=2/3 Now,n=75/(x+y). To make n maximum,x+y must be made minimum and from above,we find that min(x+y)=2+3=5 because x and y must be natural numbers.This is where I've 'unknowingly' invoked the law of GCD.(Mathematics is awesome). Finally,max(n)=75/5=15
congratulation, your solution is excellent & everybody can understand easily
lol. max pens are 30 so the max students cant be greater than 30. Now the greatest number below 30 that can be divisor of 45 with no remainder is 15.. so 15 students
The highest common factor of 45 and 30, which is the biggest number of students equally receiving pens and pencils, is 15
no comment
The prime factorizations of 3 0 and 4 5 is
3 0 = 2 × 3 × 5
4 5 = 3 2 × 5
So the Greatest Common Divisor is 3 ( 5 ) = 1 5
It's just the GCD of 30 and 45, which is 15.
What does the asymptote tell the curve?
Don't touch me.
HCF of 30 and 45. 15 students with 2 pens and 3 pencils each
To find out the answer you have to find most common multiple between 30 and 45 and the answer is 15. I am so happy that now finally I have time to solve funny quizzes and spend time on this BRILLIANT page, however it wasn't always like that I had a lot of task connected with writing essay, etc, and this web site really helped me https://aussieessaywriter.com.au/ if you have such problem. RECOMMEND YOU!
G C D ( 3 0 , 4 5 ) = 1 5
The highest common multiple of 30 and 45 is 15
G.C.D(30,45)=15.....there can be maximum of 15 students..and each student will get 2 pens and 3 pencils
X+Y=30 X-Y=45 The difference of this number is 15. Answer is 15. You can solve this way using adding metod or logic,Because only 15 students can receive the same quantity of pens and pencils.
We have 30 pens and 45 pencils. If we're to hand them out equally with none left over, we can assume that the MAXIMUM amount of students can be represented by the largest common factor of 30 and 45. This number is 15, so there can be a maximum of fifteen students.
Highest common factor. All 15 students each would receive 2 pens and 3 pencils each.
Can we solve this using Combinatorial methods? I have observed that, if we were to have 30 and/or 45 students, the Pigeonhole principle would come into play.
Since g cd ( 3 0 , 4 5 ) is 15
Therefore the maximum number of students that he could have is 15
For maximum number of equal amounts of any two or more objects will be the HIGHEST COMMON FACTOR, which in this case is 15
Look for the greatest common factor: 30 = 5 x 3 x 2 45 = 5 x 3 x 3 GCF = 5 x 3 = 15 What's left after removing the GCF from the equation is how much of each item (ie. 2 pens and 3 pencils) each student is to receive.
we find H.C.F. of 30 and 45 that is 15,so no of students is 15 ANS K.K.GARG,India
The highest common factor of 30 and 45 is 15. So, the answer is 15.
45 - 30 = 15 It is as easy as ABC
maximum diviser of 30 and 45 is 15
it's something in ratio factor to keep reminder equal Zero
30%15=0 ...... 45 %15=0
Greatest common divisor of 30 and 45 is 15.
Problem Loading...
Note Loading...
Set Loading...
Greatest Common Divisor of 30 and 45 is 15.