I am a two digit number greater than 40.You can divide me by 7 and also by 8, but not any other set of single digit number.what number am I
Multiples of 7:
49, 56, 63, 70, 77, 84, 91, 98
Multiples of 8:
48, 56, 64, 72, 80, 88, 96
Which of those numbers answer your question?
At first sight, the answer is the LCM (Lowest common multiple) of 7 and 8?
Looking further, there is a problem with the question ("but not any other set of single digit number"). Any number divisible by 8 is also divisible by 2 and 4, hence the two-digit number divisible by 7 and 8 will always be divisible by 7, 8, 4 and 2.
Thanks, Ms. Sue
Mathmate thanks that's what I thought just wanted to make sure maybe it was a misprint on the riddle.
I read the problem as the PAIR of numbers that can go into the two digit numbers. The numbers 7 and 8 are the only single digit PAIR of numbers that fit that description.
Ms Sue, I think your interpretation is very reasonable.
However, mathematically speaking, there is no limit on the number of members in a set. As Paul indicated, there is probably a misprint, where it read "but not any other SET of single digit numbers" it is probably supposed to read "but not any other PAIR of single digit numbers".
Thanks, MathMate.
To find the two-digit number that meets the given criteria, we can start by listing out the numbers greater than 40 and checking if they are divisible by both 7 and 8.
Let's go through the numbers:
- Number 41 is not divisible by 7 or 8.
- Number 42 is divisible by both 7 and 8, so it meets the criteria. However, it is a two-digit number, so it doesn't fit the requirements.
- Number 43 is not divisible by 7 or 8.
- Number 44 is not divisible by 8, so it doesn't meet the criteria.
- Number 45 is divisible by both 7 and 8, so it meets the criteria. Also, 45 is a two-digit number greater than 40, so it fits the requirements.
Therefore, the two-digit number greater than 40 that can be divided by 7 and 8, but not by any other single-digit number, is 45.