Finding Highest common factor worksheets - Math Worksheets ... - Free Printable

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:

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