Question

1. divide to find equivalent fractions for \\(\frac{6}{12}\\). first, find the factors of 6 and 12. factors of 6: \underline{\quad\quad} factors of 12: \underline{\quad\quad} the common factors of 6 and 12 are 1, \underline{\quad\quad}, \underline{\quad\quad}, and \underline{\quad\quad}

Explanation:

Step1: Find factors of 6

To find the factors of 6, we look for all positive integers that divide 6 without leaving a remainder.

• \( 6 \div 1 = 6 \), so 1 and 6 are factors.
• \( 6 \div 2 = 3 \), so 2 and 3 are factors.

So the factors of 6 are 1, 2, 3, 6.

Step2: Find factors of 12

To find the factors of 12, we look for all positive integers that divide 12 without leaving a remainder.

• \( 12 \div 1 = 12 \), so 1 and 12 are factors.
• \( 12 \div 2 = 6 \), so 2 and 6 are factors.
• \( 12 \div 3 = 4 \), so 3 and 4 are factors.

So the factors of 12 are 1, 2, 3, 4, 6, 12.

Step3: Find common factors of 6 and 12

We compare the factors of 6 (1, 2, 3, 6) and the factors of 12 (1, 2, 3, 4, 6, 12) and find the numbers that are in both lists.
The common factors are 1, 2, 3, 6.

Answer:

Factors of 6: 1, 2, 3, 6
Factors of 12: 1, 2, 3, 4, 6, 12
The common factors of 6 and 12 are 1, 2, 3, and 6.