What number is the greatest common factors of a number under 50?

Answer 1

If we are trying to find the two numbers less than 50 with the greatest common factor, we need to pick two numbers with a larger difference between them, since the greatest common factor between two numbers cannot be greatest than the difference between the two numbers. To create a large difference, we will want one number to be close in value to 50. And, for the greatest common factor, we want the other number itself to be the greatest common factor. The greatest common factor that the larger number can have (since it is larger and thus cannot be the greatest common factor itself) is the number which is half its value.

So, if we choose the even number closest in value to 50, we get 48. Then, if we take half of it, we get 24. The greatest common factor of 24 and 48 is 24. This is the largest possible greatest common factor of a pair of numbers less than 50.