Sure! Let's address part (a) of the question by detailing the step-by-step process for finding the common factors of 25 and 45.
### (a) Find the common factors of 25 and 45
1. List the factors of 25:
- A factor is a number that divides into another number without leaving a remainder.
- The factors of 25 are: 1, 5, 25 (since 1 25 = 25 and 5 5 = 25).
Factors of 25: [tex]\(\{1, 5, 25\}\)[/tex]
2. List the factors of 45:
- Similarly, we need to find numbers that divide 45 without leaving a remainder.
- The factors of 45 are: 1, 3, 5, 9, 15, 45 (since 1 45 = 45, 3 15 = 45, and 5 * 9 = 45).
Factors of 45: [tex]\(\{1, 3, 5, 9, 15, 45\}\)[/tex]
3. Identify the common factors:
- To find the common factors, we compare the lists of factors for both numbers and find the common elements.
Comparing the factors:
- Factors of 25: [tex]\(\{1, 5, 25\}\)[/tex]
- Factors of 45: [tex]\(\{1, 3, 5, 9, 15, 45\}\)[/tex]
Common factors: [tex]\(\{1, 5\}\)[/tex]
So, the common factors of 25 and 45 are 1 and 5.
When you need the solutions for part (b), please provide the numbers and I’ll help you find their common factors as well.
