What is the common factor of 12 and 18

General
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what is the common factor of 12 and 18

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What is the common factor of 12 and 18?

To determine the common factors of 12 and 18, it’s essential first to understand what factors are and then find the shared factors for these two numbers.

Step-by-Step Solution:

  1. List the factors of each number:

    • Factors of 12:

      • A factor is a number that divides another number without leaving a remainder.
      • The factors of 12 are computed as follows:
        \begin{align*} 12 \div 1 &= 12 \quad (\text{1 is a factor}) \\ 12 \div 2 &= 6 \quad (\text{2 is a factor}) \\ 12 \div 3 &= 4 \quad (\text{3 is a factor}) \\ 12 \div 4 &= 3 \quad (\text{4 is a factor}) \\ 12 \div 6 &= 2 \quad (\text{6 is a factor}) \\ 12 \div 12 &= 1 \quad (\text{12 is a factor}) \end{align*}
      • Therefore, the factors of 12 are: 1, 2, 3, 4, 6, 12.

    • Factors of 18:

      • Similarly, the factors of 18 are computed as follows:
        \begin{align*} 18 \div 1 &= 18 \quad (\text{1 is a factor}) \\ 18 \div 2 &= 9 \quad (\text{2 is a factor}) \\ 18 \div 3 &= 6 \quad (\text{3 is a factor}) \\ 18 \div 6 &= 3 \quad (\text{6 is a factor}) \\ 18 \div 9 &= 2 \quad (\text{9 is a factor}) \\ 18 \div 18 &= 1 \quad (\text{18 is a factor}) \end{align*}
      • Therefore, the factors of 18 are: 1, 2, 3, 6, 9, 18.

  2. Identify the common factors:

    • Common factors are those that appear in the factor lists of both numbers.

    By comparing the factors of 12 and 18:

    • Factors of 12: 1, 2, 3, 4, 6, 12
    • Factors of 18: 1, 2, 3, 6, 9, 18

    The common factors of 12 and 18 are: 1, 2, 3, 6.

Conclusion:

The common factors of 12 and 18 are 1, 2, 3, and 6. Among these, the greatest common factor (GCF) or greatest common divisor (GCD) is 6. These common factors indicate the numbers that can exactly divide both 12 and 18 without leaving a remainder.

Therefore, when asked, “What is the common factor of 12 and 18?”, you can confidently respond that the common factors are 1, 2, 3, and 6.