To find a number that is both a factor of 450 and a multiple of 25, we first need to break down what these terms mean:
Factors of 450: A factor is a number that divides another number without leaving a remainder. The factors of 450 can be calculated by identifying the numbers that divide 450 evenly.
Multiples of 25: A multiple of 25 is any number that can be expressed as 25 times an integer. This includes numbers like 25, 50, 75, 100, and so on.
Now, let’s look at the factors of 450. The prime factorization of 450 is:
- 450 = 2 × 3² × 5²
From this, we can find the complete list of factors of 450 by considering the various combinations of these prime factors:
- 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Next, we check which of these factors are also multiples of 25:
- 25 (25 x 1)
- 50 (25 x 2)
- 75 (25 x 3)
- 150 (25 x 6)
- 450 (25 x 18)
Thus, the numbers that are both factors of 450 and multiples of 25 are:
- 25
- 50
- 75
- 150
- 450
In conclusion, the factors of 450 that are also multiples of 25 include 25, 50, 75, 150, and 450.