CODEWITHSUNDEEP
javamathdivision
GrumpyKitten
GrumpyKitten

Reputation: 35

Number of multiples of x in a range for large numbers

This is simple mathematics I guess, but I just can't figure it out + I'm new to coding. I need to find out how many numbers are divisible by x in a range. Here's an example: I need to find how many numbers in the range 11 to 30 are divisible by 3. The answer is 7, and I already coded it:

while (a <= b) {
    if (a % 3 == 0) {
        c++;
        a++;
    else {
        a++;
    }
}

HOWEVER, this works horribly for large numbers as I check every single number. I tried doing c = (b-a)/3, but obviously this doesn't work for all examples, just like it doesn't for the one above. So, could you please help me find some sort of a simple equation that would calculate this for me. I'm feeling so stupid for not being able to figure this one out.

Upvotes: 1

Views: 993

Answers (2)

Yu Hao
Yu Hao

Reputation: 122493

In psudo-code:

  1. Calculate the smallest number divisible by 3 that is bigger than a: c = math.ceil(a / 3) * 3.
  2. Calculate the biggest number divisible by 3 that is smaller than b: d = math.floor(b / 3) * 3.
  3. The answer is (d - c) / 3 + 1.

In the example of 11 to 30, c is 12, and d is 30, the final answer is 7.

Upvotes: 2

velocirabbit
velocirabbit

Reputation: 706

You're close! Do something like (no idea what you're coding in so this will be pseudo-code):

function numDiv(int a, int b, int divBy) {
int x;
if(a>b) x=1+a-b;
else x=1+b-a;
return floor(x/divBy);
}

the floor and +1 will should get you there.

Upvotes: 0

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