Multiples 3 digit numbers

First, note that $9$ is a valid possibility when, for example, $9*111 = 999$ .

Any number from $10$ and beyond, when multiplied by a $3$ -digit number becomes a number greater than or equal to $1000$ , and so $N$ would be a $4$ -digit number which would not meet the problem's requirements.

observe that when you multiply a 3digit number by 10, you get a 4digit number. Therefore, the largest possible value of $\frac{m}{n}$ is $9$

The biggest 3 digit no=999 The smallest 3 digit no=100 999/100=9.99 Hence, the largest possible value is 9

M and N are both 3 digit numbers, so they can range from 100 to 999. The highest possible number for the equation would be 999/100 but that will not equal an integer so you will increase the number to 999/111 and that will equal 9

100 9=900 this is an example but you can go farther Since 100 is the smallest 3didgit number, 100 10=1000. 1000 is a four digit number. Therefore 9 is the highest

100<=M<1000 so 2<=logM<3 and 100<=N<100 so 2<=logN<3 or -3<-logN<=-2. Adding theses inequalities gives -1<logM-logN<1 or -1<log(M/N)<1 or 1/10<M/N<10. Since M/N is an integer,1<= M/N<=9. We can easily find examples of M/N=9 (M=900, N=100), but we will search in vain to find an example where M/N=10.

The greatest 3 digit integer is 999 and the smallest is 100. However, because we are looking for integers and also dividing by 100 we know that we can only use exact three digit multiples of 100; the greatest of those multiples being 900. Therefore,

900/100 = 9

Python 2.7:

1
2
3
4
5
6
7

biggest = 0
for m in xrange(100,1000):
    for n in xrange(100,1000):
        if m % n == 0:
            if m/n > biggest:
                biggest = m/n
print "Answer:", biggest

Pythonic solution

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

'POSSIBILITY ESTIMATOR'

nos = range(100, 1000)
nos2 = range(100, 1000)
possible = list()

for i in nos:
    for j in nos2:
        if i % j == 0:
            possible.append(i / j)

print list(set(possible))[-1]

Largest 3 digit no 999 Smalest 111 to have integer ratioo 999/111=9

Divide the largest 3-digit number by the smallest 3-digit number. So, 999÷100=9.

In order to get a possible answer I just devided biggest 3 digit number possible and smallest three digit number possible. Thus, 999/111 =9

Choose the highest possible 3 digit whole number and substitute it for M. So M=999. Then, you need to find what is N. Easy. Just divide 999 by 9. Why 9 for N? Because it's probably the only whole number you can use that will divide 999 without turning the quotient into a decimal number that will keep it a 3 digit number.

M=999 N=111
M/N=999/111

999/111=9

M is 999, and n can be 111

I just multiplied 3 times 3