Respuesta :
Answer:
5
Step-by-step explanation:
27/n=quotient + 3/n
n cannot be less than or equal to 3.
n=4 gives 27/4=6+3/4
n=5 gives 27/5=5+2/5
n=6 gives 27/6=4+3/6
n=7 gives 27/7=4+2/7
n=8 gives 27/8=3+3/8
n=9 gives 27/9=3+0/9
n=10 gives 27/10=2+7/10
n=11 gives 27/11=2+5/11
n=12 gives 27/12=2+3/12
n=13 gives 27/13=2+1/13
n=14 gives 27/14=1+13/14
n=15 gives 27/15=1+12/15
n=16 gives 27/16=1+11/16
n=17 gives 27/17=1+10/17
n=18 gives 27/18=1+9/18
n=19 gives 27/19=1+8/19
n=20 gives 27/20=1+7/20
n=21 gives 27/21=1+6/21
n=22 gives 27/22=1+5/22
n=23 gives 27/23=1+4/23
n=24 gives 27/24=1+3/24
n=25 gives 27/25=1+2/25
n=26 gives 27/26=1+1/26
n=27 gives 27/27=1+0/27
n=28 gives 27/28=0+27/28
So n can't be bigger than or equal to 27.
Let's count the one's above with remainder 3....
I think I counted 5.
27/n=q+3/n
27=nq+3
Subtract 3 on both sides
24=nq
So the pairs of numbers with product 24 are:
1(24)
2(12)
3(8)
4(6)
So n could equal 1,2,3,4,6,8,12, or 24.
If we want a remainder of 3, n cannot be 1,2, or 3.
Actually, if you look above we found these were the n that gave us remainder 3 when dividing by n.
Solving this question will involve basic division knowledge.
The different positive integer values of n are; 4,6,8,12,24
From knowledge on division, we know that when 27 is divided by N and we have 3 as remainder, we can express it as;
[tex]\frac{27}{n}[/tex] = quotient + [tex]\frac{3}{n}[/tex]
Now let us rearrange to get;
[tex]\frac{27}{n}[/tex] - [tex]\frac{3}{n}[/tex] = quotient
this gives;
[tex]\frac{24}{n}[/tex] = quotient
Now to get how many positive integers can be n, it means all positive values of the quotient must be positive integers as well.
Factors of 24 are; 1, 2, 3, 4, 6, 8, 12, 24
Thus, the possible positive integers will come from this list.
But we can't make use of 1,2,3 as possible values of n because when we divide with 27, we will get either an exact value or 1 as the remainder.
Thus the possible positive integer values of n are; 4,6,8,12,24
Read more at; brainly.in/question/20088076
