# Thread: What is the third number common to two other numbers

1. ## What is the third number common to two other numbers

There are 3 numbers, a, b, c, and 2 divisors e, and f.
a and c are one pair, and b and c are another pair. c is common to both pairs.
e is the divisor of a and c which gives a number with the same remainder.
f is the divisor of b and c which gives a number with the same remainder.

Example:
a= 1100 b= 678 c= 500 e= 200 f= 89

Now a/e and c/e (Pair 1)
1100/200 = 5.5
500/200 = 2.5
common remainder of 0.5

Now b/f and c/f (Pair 2)
678/89 = 7.61
500/89 = 5.61
common remainder of 0.61

Question; Can there be more than one value for e and f ?
If a and b are known, can you calculate c ? How ?

I don't know where to start on this. Your help and suggestions are needed.
Thank you.

2. ## Re: What is the third number common to two other numbers

a>b>c ? e<>f ?

a=10, b=8, c=6, e=2, f=2 : that's valid according to your post: ALL have remainder = 0.

Example where a,b,c are same at least twice:
a=16, b=15, c=12, e=2, f=3
a=16, b=15, c=12, e=4, f=3
Was that your "is it possible" question ?

3. ## Re: What is the third number common to two other numbers

Originally Posted by Wilmer
a>b>c ? e<>f ?

a=10, b=8, c=6, e=2, f=2 : that's valid according to your post: ALL have remainder = 0.

Example where a,b,c are same at least twice:
a=16, b=15, c=12, e=2, f=3
a=16, b=15, c=12, e=4, f=3
Was that your "is it possible" question ?
Oops,
a<>b<>c and e<>f
a, b, or c could be a prime.
Any solution should be able to solve all possible values of a, b, c.

4. ## Re: What is the third number common to two other numbers

Originally Posted by Duncan
a<>b<>c and e<>f
a, b, or c could be a prime.
Any solution should be able to solve all possible values of a, b, c.