Printable math worksheet for finding the Greatest Common Factor (GCF) using the long division method.

To solve the problem of finding the Greatest Common Factor (GCF) using the long division method, we will follow these steps for each pair of numbers:

Steps to Find GCF Using Long Division:

1. Divide the larger number by the smaller number.
2. If there is a remainder, divide the divisor by the remainder.
3. Repeat this process until the remainder is zero.
4. The last non-zero remainder is the GCF.

Let's solve each problem step by step.

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1. \( 45, 55 \)

- Divide 55 by 45:
\( 55 ÷ 45 = 1 \) remainder \( 10 \).
- Now divide 45 by 10:
\( 45 ÷ 10 = 4 \) remainder \( 5 \).
- Now divide 10 by 5:
\( 10 ÷ 5 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 5 \).
GCF = 5

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2. \( 30, 60 \)

- Divide 60 by 30:
\( 60 ÷ 30 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 30 \).
GCF = 30

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3. \( 12, 40 \)

- Divide 40 by 12:
\( 40 ÷ 12 = 3 \) remainder \( 4 \).
- Now divide 12 by 4:
\( 12 ÷ 4 = 3 \) remainder \( 0 \).

The last non-zero remainder is \( 4 \).
GCF = 4

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4. \( 36, 75 \)

- Divide 75 by 36:
\( 75 ÷ 36 = 2 \) remainder \( 3 \).
- Now divide 36 by 3:
\( 36 ÷ 3 = 12 \) remainder \( 0 \).

The last non-zero remainder is \( 3 \).
GCF = 3

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5. \( 44, 58 \)

- Divide 58 by 44:
\( 58 ÷ 44 = 1 \) remainder \( 14 \).
- Now divide 44 by 14:
\( 44 ÷ 14 = 3 \) remainder \( 2 \).
- Now divide 14 by 2:
\( 14 ÷ 2 = 7 \) remainder \( 0 \).

The last non-zero remainder is \( 2 \).
GCF = 2

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6. \( 33, 39 \)

- Divide 39 by 33:
\( 39 ÷ 33 = 1 \) remainder \( 6 \).
- Now divide 33 by 6:
\( 33 ÷ 6 = 5 \) remainder \( 3 \).
- Now divide 6 by 3:
\( 6 ÷ 3 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 3 \).
GCF = 3

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7. \( 28, 44 \)

- Divide 44 by 28:
\( 44 ÷ 28 = 1 \) remainder \( 16 \).
- Now divide 28 by 16:
\( 28 ÷ 16 = 1 \) remainder \( 12 \).
- Now divide 16 by 12:
\( 16 ÷ 12 = 1 \) remainder \( 4 \).
- Now divide 12 by 4:
\( 12 ÷ 4 = 3 \) remainder \( 0 \).

The last non-zero remainder is \( 4 \).
GCF = 4

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8. \( 30, 75 \)

- Divide 75 by 30:
\( 75 ÷ 30 = 2 \) remainder \( 15 \).
- Now divide 30 by 15:
\( 30 ÷ 15 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 15 \).
GCF = 15

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9. \( 25, 40 \)

- Divide 40 by 25:
\( 40 ÷ 25 = 1 \) remainder \( 15 \).
- Now divide 25 by 15:
\( 25 ÷ 15 = 1 \) remainder \( 10 \).
- Now divide 15 by 10:
\( 15 ÷ 10 = 1 \) remainder \( 5 \).
- Now divide 10 by 5:
\( 10 ÷ 5 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 5 \).
GCF = 5

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10. \( 75, 90 \)

- Divide 90 by 75:
\( 90 ÷ 75 = 1 \) remainder \( 15 \).
- Now divide 75 by 15:
\( 75 ÷ 15 = 5 \) remainder \( 0 \).

The last non-zero remainder is \( 15 \).
GCF = 15

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11. \( 60, 75 \)

- Divide 75 by 60:
\( 75 ÷ 60 = 1 \) remainder \( 15 \).
- Now divide 60 by 15:
\( 60 ÷ 15 = 4 \) remainder \( 0 \).

The last non-zero remainder is \( 15 \).
GCF = 15

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12. \( 50, 60 \)

- Divide 60 by 50:
\( 60 ÷ 50 = 1 \) remainder \( 10 \).
- Now divide 50 by 10:
\( 50 ÷ 10 = 5 \) remainder \( 0 \).

The last non-zero remainder is \( 10 \).
GCF = 10

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13. \( 40, 80 \)

- Divide 80 by 40:
\( 80 ÷ 40 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 40 \).
GCF = 40

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14. \( 18, 81 \)

- Divide 81 by 18:
\( 81 ÷ 18 = 4 \) remainder \( 9 \).
- Now divide 18 by 9:
\( 18 ÷ 9 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 9 \).
GCF = 9

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15. \( 60, 90 \)

- Divide 90 by 60:
\( 90 ÷ 60 = 1 \) remainder \( 30 \).
- Now divide 60 by 30:
\( 60 ÷ 30 = 2 \) remainder \( 0 \).

The last non-zero remainder is \( 30 \).
GCF = 30

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 5 \\
2. & 30 \\
3. & 4 \\
4. & 3 \\
5. & 2 \\
6. & 3 \\
7. & 4 \\
8. & 15 \\
9. & 5 \\
10. & 15 \\
11. & 15 \\
12. & 10 \\
13. & 40 \\
14. & 9 \\
15. & 30 \\
\end{array}
}
\]