Factor the linear expression 30 d + 24 using the GCF
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To factor the linear expression \(30d + 24\) using the greatest common factor (GCF), first, we need to determine the GCF of the coefficients \(30\) and \(24\).
1. **Find the GCF of 30 and 24**:
- The factors of \(30\) are: \(1, 2, 3, 5, 6, 10, 15, 30\)
- The factors of \(24\) are: \(1, 2, 3, 4, 6, 8, 12, 24\)
- The common factors are: \(1, 2, 3, 6\)
- The greatest common factor is \(6\).
2. **Factor out the GCF**:
- Divide each term in the expression by the GCF:
- \(30d \div 6 = 5d\)
- \(24 \div 6 = 4\)
3. **Write the factored expression**:
\[
30d + 24 = 6(5d + 4)
\]
Thus, the factored form of \(30d + 24\) using the GCF is:
\[
6(5d + 4)
\]
1. **Find the GCF of 30 and 24**:
- The factors of \(30\) are: \(1, 2, 3, 5, 6, 10, 15, 30\)
- The factors of \(24\) are: \(1, 2, 3, 4, 6, 8, 12, 24\)
- The common factors are: \(1, 2, 3, 6\)
- The greatest common factor is \(6\).
2. **Factor out the GCF**:
- Divide each term in the expression by the GCF:
- \(30d \div 6 = 5d\)
- \(24 \div 6 = 4\)
3. **Write the factored expression**:
\[
30d + 24 = 6(5d + 4)
\]
Thus, the factored form of \(30d + 24\) using the GCF is:
\[
6(5d + 4)
\]
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