Question
REMEMBER 4. Use the associative property to find factors of 60. \[ \begin{aligned} 60 & =6 \times 10 \\ & =(3 \times \ldots) \times(2 \times \ldots) \\ & =(2 \times 2) \times(3 \times \ldots \\ & =4 \times \\ & =\end{aligned} \] Some factors of 60 are
Ask by Martin Sanders. in the United States
Jan 22,2025
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Answer
Some factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Solution
Certainly! Let's continue using the associative property to find factors of 60 by completing the steps you provided:
\[
\begin{aligned}
60 &= 6 \times 10 \\
&= (3 \times 2) \times (2 \times 5) \\
&= (2 \times 2) \times (3 \times 5) \\
&= 4 \times 15 \\
&= 4 \times (3 \times 5) \\
&= 2^2 \times 3 \times 5 \\
\end{aligned}
\]
**Some factors of 60 are:**
- **1** (since \(1 \times 60 = 60\))
- **2** (since \(2 \times 30 = 60\))
- **3** (since \(3 \times 20 = 60\))
- **4** (since \(4 \times 15 = 60\))
- **5** (since \(5 \times 12 = 60\))
- **6** (since \(6 \times 10 = 60\))
- **10** (since \(10 \times 6 = 60\))
- **12** (since \(12 \times 5 = 60\))
- **15** (since \(15 \times 4 = 60\))
- **20** (since \(20 \times 3 = 60\))
- **30** (since \(30 \times 2 = 60\))
- **60** (since \(60 \times 1 = 60\))
So, the complete list of factors of 60 is:
\[ 1, \, 2, \, 3, \, 4, \, 5, \, 6, \, 10, \, 12, \, 15, \, 20, \, 30, \, 60 \]
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Simplify this solution Beyond the Answer
To uncover the factors of 60 using the associative property, start by expressing 60 as \(6 \times 10\). Next, break it down: \(6\) can be further factored into \(3 \times 2\), and \(10\) can be factored into \(5 \times 2\). So, we have: \[ 60 = (3 \times 2) \times (5 \times 2) \] Rearranging gives \(60 = (3 \times 2 \times 2) \times 5\) or \(60 = 4 \times 15\). Several factors of 60 that emerge from this are: \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\). Isn’t factorization like a fun puzzle where each piece fits neatly together?
