Understanding the Factors of the Given Expression
To find the factors of the expression comprising the terms:
- 15xy
- 45x
- 6y
- 18y
- 2
- 5x
- 3
- 5x
- 2y
- 6
We will first determine the prime factorization of each term:
Prime Factorization
- 15xy: 3 × 5 × x × y
- 45x: 3² × 5 × x
- 6y: 2 × 3 × y
- 18y: 2 × 3² × y
- 2: 2
- 5x: 5 × x
- 3: 3
- 5x: 5 × x (same as above)
- 2y: 2 × y
- 6: 2 × 3
Common Factors
Now we’ll look for the common factors among these terms:
- From 15xy: 3, 5, x, y
- From 45x: 3, 5, x
- From 6y: 2, 3, y
- From 18y: 2, 3, y
- From 2: 2
- From 5x: 5, x
- From 3: 3
- From 5x: 5, x (again)
- From 2y: 2, y
- From 6: 2, 3
The common prime factors among all these terms are 2, 3, and 5.
Conclusion
The common factors present in the complete expression are:
- 1 (unity)
- 2
- 3
- 5
- 6
- 15
- 30 (which is a product of 2, 3, and 5)
Thus, the factors of the combined expression are determined.