Grade 7 Maths Revision worksheet featuring problems on listing factors, finding the greatest common factor, and determining the lowest common multiple.

Problem Explanation and Solution

The worksheet is divided into three sections:
1. List the factors for each number.
2. Find the greatest common factor (GCF) for each set of numbers.
3. Find the lowest common multiple (LCM) for each set of numbers.

Let's solve each section step by step.

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Section 1: List the factors for each number.

#### Step-by-Step Solution:
To find the factors of a number, list all the numbers that divide the given number evenly (without leaving a remainder).

1. 55:
Factors: \(1, 5, 11, 55\)

2. 3:
Factors: \(1, 3\)

3. 24:
Factors: \(1, 2, 3, 4, 6, 8, 12, 24\)

4. 94:
Factors: \(1, 2, 47, 94\)

5. 45:
Factors: \(1, 3, 5, 9, 15, 45\)

6. 1:
Factors: \(1\)

7. 6:
Factors: \(1, 2, 3, 6\)

8. 7:
Factors: \(1, 7\)

9. 78:
Factors: \(1, 2, 3, 6, 13, 26, 39, 78\)

10. 4:
Factors: \(1, 2, 4\)

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Section 2: Find the greatest common factor (GCF) for each set of numbers.

#### Step-by-Step Solution:
To find the GCF of two numbers, list the factors of each number and identify the largest factor that is common to both.

11. 15 and 35:
- Factors of 15: \(1, 3, 5, 15\)
- Factors of 35: \(1, 5, 7, 35\)
- Common factors: \(1, 5\)
- GCF: \(5\)

12. 50 and 35:
- Factors of 50: \(1, 2, 5, 10, 25, 50\)
- Factors of 35: \(1, 5, 7, 35\)
- Common factors: \(1, 5\)
- GCF: \(5\)

13. 93 and 48:
- Factors of 93: \(1, 3, 31, 93\)
- Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)
- Common factors: \(1, 3\)
- GCF: \(3\)

14. 44 and 33:
- Factors of 44: \(1, 2, 4, 11, 22, 44\)
- Factors of 33: \(1, 3, 11, 33\)
- Common factors: \(1, 11\)
- GCF: \(11\)

15. 46 and 74:
- Factors of 46: \(1, 2, 23, 46\)
- Factors of 74: \(1, 2, 37, 74\)
- Common factors: \(1, 2\)
- GCF: \(2\)

16. 70 and 90:
- Factors of 70: \(1, 2, 5, 7, 10, 14, 35, 70\)
- Factors of 90: \(1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90\)
- Common factors: \(1, 2, 5, 10\)
- GCF: \(10\)

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Section 3: Find the lowest common multiple (LCM) for each set of numbers.

#### Step-by-Step Solution:
To find the LCM of two numbers, use the formula:
\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCF}(a, b)}
\]
Alternatively, list the multiples of each number and identify the smallest multiple that is common to both.

17. 8 and 7:
- Multiples of 8: \(8, 16, 24, 32, 40, 56, \ldots\)
- Multiples of 7: \(7, 14, 21, 28, 35, 42, 49, 56, \ldots\)
- Common multiples: \(56\)
- LCM: \(56\)

18. 9 and 10:
- Multiples of 9: \(9, 18, 27, 36, 45, 54, 63, 72, 81, 90, \ldots\)
- Multiples of 10: \(10, 20, 30, 40, 50, 60, 70, 80, 90, \ldots\)
- Common multiples: \(90\)
- LCM: \(90\)

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Final Answers:

1. Factors:
1. \(55\): \(1, 5, 11, 55\)
2. \(3\): \(1, 3\)
3. \(24\): \(1, 2, 3, 4, 6, 8, 12, 24\)
4. \(94\): \(1, 2, 47, 94\)
5. \(45\): \(1, 3, 5, 9, 15, 45\)
6. \(1\): \(1\)
7. \(6\): \(1, 2, 3, 6\)
8. \(7\): \(1, 7\)
9. \(78\): \(1, 2, 3, 6, 13, 26, 39, 78\)
10. \(4\): \(1, 2, 4\)

2. Greatest Common Factor (GCF):
11. \(15\) and \(35\): \(5\)
12. \(50\) and \(35\): \(5\)
13. \(93\) and \(48\): \(3\)
14. \(44\) and \(33\): \(11\)
15. \(46\) and \(74\): \(2\)
16. \(70\) and \(90\): \(10\)

3. Lowest Common Multiple (LCM):
17. \(8\) and \(7\): \(56\)
18. \(9\) and \(10\): \(90\)

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Boxed Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Factors:} & \\
1. & 1, 5, 11, 55 \\
2. & 1, 3 \\
3. & 1, 2, 3, 4, 6, 8, 12, 24 \\
4. & 1, 2, 47, 94 \\
5. & 1, 3, 5, 9, 15, 45 \\
6. & 1 \\
7. & 1, 2, 3, 6 \\
8. & 1, 7 \\
9. & 1, 2, 3, 6, 13, 26, 39, 78 \\
10. & 1, 2, 4 \\
\\
\text{GCF:} & \\
11. & 5 \\
12. & 5 \\
13. & 3 \\
14. & 11 \\
15. & 2 \\
16. & 10 \\
\\
\text{LCM:} & \\
17. & 56 \\
18. & 90 \\
\end{array}
}
\]