To determine which number is both a factor of 450 and a multiple of 25, we first need to identify the factors of 450. The factors are numbers that can divide 450 without leaving a remainder.
The prime factorization of 450 is:
- 450 = 2 × 3² × 5²
From this, we can list the factors of 450, which include 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, and 450.
Next, we look for multiples of 25. The multiples of 25 include numbers like 25, 50, 75, 100, 125, and so on.
Now, we can see which of the factors of 450 are also multiples of 25. From our list, 25, 50, and 75 meet this criteria. Therefore, the factors of 450 that are multiples of 25 are:
- 25
- 50
- 75
Keenly, 50 and 75 are both factors of 450 and multiples of 25. Thus, any of these numbers can be considered correct depending on the options given in your question.