The factors of a number include 2, 3, 4, 6, 8, 12, 16, 32, and 48. Which could be the number?
To determine the possible number, we can look for the greatest common divisor (GCD) of all these factors. The GCD is the largest number that divides all the given factors evenly.
There are two ways to find the GCD:
1. Prime Factorization:
- Find the prime factorization of each factor.
- List the common prime factors with their smallest exponent.
- Multiply these common prime factors together to find the GCD.
2. Listing Factors:
- Start with the smallest common factor and continue to the largest common factor.
- Check if each number is a factor of all the given factors.
- The largest number that is a factor of all the given factors is the GCD.
For this question, let's use the second method:
Starting with the smallest common factor, we have:
- 2 is a factor of all the given factors.
- 3 is a factor of all the given factors.
- 4 is a factor of all the given factors.
- 6 is a factor of all the given factors.
- 8 is a factor of all the given factors.
- 12 is a factor of all the given factors.
- 16 is a factor of all the given factors.
- 32 is a factor of all the given factors.
- 48 is a factor of all the given factors.
The largest number that is a factor of all these factors is 48.
Therefore, the possible number could be 48.