Printable math worksheet for identifying factors of given numbers, designed for primary education.

Problem Description:

The task is to identify and color the factors of specific numbers from a given list. The numbers are 15, 28, 36, 52, 66, and 45. A factor of a number is any integer that divides the number evenly without leaving a remainder.

Solution Approach:

1. Understand Factors: A factor of a number \( n \) is any integer \( f \) such that \( n \div f \) results in an integer.
2. List All Possible Factors: For each number, determine all integers that divide it evenly.
3. Identify Factors in the Grid: Check which numbers in the grid are factors of the given number and mark them.

Step-by-Step Solution:

#### 1. Factors of 15
- Possible factors: \( 1, 3, 5, 15 \)
- Numbers in the grid: \( 1, 4, 5, 9, 8, 11, 3, 25, 12, 15 \)
- Factors in the grid: \( 1, 3, 5, 15 \)

#### 2. Factors of 28
- Possible factors: \( 1, 2, 4, 7, 14, 28 \)
- Numbers in the grid: \( 6, 28, 5, 4, 8, 2, 3, 1, 14, 7 \)
- Factors in the grid: \( 1, 2, 4, 7, 14, 28 \)

#### 3. Factors of 36
- Possible factors: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- Numbers in the grid: \( 12, 4, 18, 13, 36, 6, 2, 3, 1, 9 \)
- Factors in the grid: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)

#### 4. Factors of 52
- Possible factors: \( 1, 2, 4, 13, 26, 52 \)
- Numbers in the grid: \( 1, 2, 8, 13, 17, 26, 4, 12, 52, 7 \)
- Factors in the grid: \( 1, 2, 4, 13, 26, 52 \)

#### 5. Factors of 66
- Possible factors: \( 1, 2, 3, 6, 11, 22, 33, 66 \)
- Numbers in the grid: \( 12, 2, 33, 6, 66, 1, 3, 13, 11, 22 \)
- Factors in the grid: \( 1, 2, 3, 6, 11, 22, 33, 66 \)

#### 6. Factors of 45
- Possible factors: \( 1, 3, 5, 9, 15, 45 \)
- Numbers in the grid: \( 45, 20, 3, 9, 15, 5, 1, 35, 8, 10 \)
- Factors in the grid: \( 1, 3, 5, 9, 15, 45 \)

Final Answer:

The factors to be colored for each number are:

- 15: \( 1, 3, 5, 15 \)
- 28: \( 1, 2, 4, 7, 14, 28 \)
- 36: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- 52: \( 1, 2, 4, 13, 26, 52 \)
- 66: \( 1, 2, 3, 6, 11, 22, 33, 66 \)
- 45: \( 1, 3, 5, 9, 15, 45 \)

\[
\boxed{
\begin{array}{l}
\text{15: } 1, 3, 5, 15 \\
\text{28: } 1, 2, 4, 7, 14, 28 \\
\text{36: } 1, 2, 3, 4, 6, 9, 12, 18, 36 \\
\text{52: } 1, 2, 4, 13, 26, 52 \\
\text{66: } 1, 2, 3, 6, 11, 22, 33, 66 \\
\text{45: } 1, 3, 5, 9, 15, 45 \\
\end{array}
}
\]