Theory:
Common factor
When we find factors for two or more numbers if any factors are common (same) between the numbers, they are called common factors.
Example:
1. Find the common factors of \(8\) and \(24\).
| \(1 \times 8 = 8\) | \(2 \times 4 = 8\) | \(4 \times 2 = 8\) |
We stop here because \(2\) and \(4\) already exist as a factor.
| \(1 \times 24 = 24\) | \(2 \times 12 = 24\) | \(3 \times 8 = 24\) | \(4 \times 6 = 24\) | \(6 \times 4 = 24\) |
We stop here because \(4\) and \(6\) already exist as a factor.
Common factors of \(8\) and \(24\) are \(1\), \(2\), \(4\) and \(8\).
2. Find common factors of \(15\), \(45\) and \(50\).
| \(1 \times 15 = 15\) | \(3 \times 5 = 15\) | \(5 \times 3 = 15\) |
We stop here because \(3\) and \(5\) already exist as a factor.
| \(1 \times 45 = 45\) | \(3 \times 15 = 45\) | \(5 \times 9 = 45\) | \(9 \times 5 = 45\) |
We stop here because \(5\) and \(9\) already exist as a factor.
| \(1 \times 50 = 50\) | \(2 \times 25 = 50\) | \(5 \times 10 = 50\) | \(10 \times 5 = 50\) |
We stop here because \(5\) and \(10\) already exist as a factor.
Common factors of \(15\), \(45\) and \(50\) are \(1\) and \(5\).