1. The problem asks us to use the associative property to find factors of 60.
2. The associative property states that when multiplying three or more numbers, the way in which the numbers are grouped does not change the product. Mathematically, this is:
$$ (a \times b) \times c = a \times (b \times c) $$
3. Start with the given factorization:
$$ 60 = 6 \times 10 $$
4. Apply the associative property by breaking down 6 and 10 into their factors:
$$ 6 = 3 \times 2, \quad 10 = 2 \times 5 $$
So,
$$ 60 = (3 \times 2) \times (2 \times 5) $$
5. Regroup the factors using the associative property:
$$ (3 \times 2) \times (2 \times 5) = (3 \times (2 \times 2)) \times 5 = (3 \times 4) \times 5 $$
6. This shows another factorization:
$$ 60 = 4 \times 15 $$
7. We can also write:
$$ 60 = 6 \times 10 $$
8. From these factorizations, the factors of 60 include:
$$ 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 $$
These are all the numbers that multiply in pairs to give 60.
Final answer: The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Associative Factors F373B3
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.