Question

27 divided by N has a remainder of 3. How many different positive integers could n be?

Answer 1

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.

Answer 2

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;

$\frac{27}{n}$ = quotient + $\frac{3}{n}$

Now let us rearrange to get;

$\frac{27}{n}$ - $\frac{3}{n}$ = quotient

this gives;

$\frac{24}{n}$ = 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