What is the greatest common factor of 100 and 50?
The correct answer and explanation is:
The greatest common factor (GCF) of 100 and 50 is 50.
Explanation:
To find the greatest common factor, we need to list the factors of both numbers and identify the largest number that appears in both lists.
- Factors of 100: The factors of 100 are all the numbers that divide into 100 exactly. These factors are:
- 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 50: The factors of 50 are all the numbers that divide into 50 exactly. These factors are:
- 1, 2, 5, 10, 25, 50
Now, by comparing the two lists of factors, we can see that the common factors are:
- 1, 2, 5, 10, 25, 50
The greatest of these common factors is 50.
Another Method: Prime Factorization
Another way to find the GCF is by using prime factorization. We break both numbers down into their prime factors:
- Prime factorization of 100:
- 100 = 2 × 2 × 5 × 5 = 22×522^2 \times 5^2
- Prime factorization of 50:
- 50 = 2 × 5 × 5 = 21×522^1 \times 5^2
To find the GCF, we take the lowest power of each prime factor that appears in both factorizations:
- The lowest power of 2 is 212^1.
- The lowest power of 5 is 525^2.
Therefore, the GCF is 21×52=2×25=502^1 \times 5^2 = 2 \times 25 = 50.
Conclusion:
Both methods show that the greatest common factor of 100 and 50 is 50. This is the largest number that can divide both 100 and 50 without leaving a remainder.