Question

list all the common factors of each pair of numbers:
(13) 14. 15 and 18
(13) 15. 36 and 45
(13) 16. 9 and 10

Explanation:

Step1: Understand Common Factors

Common factors are numbers that divide both given numbers without leaving a remainder. We'll find the factors of each number and then identify the common ones.

Step2: Solve for 15 and 18

• Factors of 15: $1, 3, 5, 15$ (since $1\times15 = 15$, $3\times5 = 15$)
• Factors of 18: $1, 2, 3, 6, 9, 18$ (since $1\times18 = 18$, $2\times9 = 18$, $3\times6 = 18$)
• Common factors: $1, 3$ (numbers present in both factor lists)

Step3: Solve for 36 and 45

• Factors of 36: $1, 2, 3, 4, 6, 9, 12, 18, 36$ ( $1\times36 = 36$, $2\times18 = 36$, $3\times12 = 36$, $4\times9 = 36$, $6\times6 = 36$)
• Factors of 45: $1, 3, 5, 9, 15, 45$ ( $1\times45 = 45$, $3\times15 = 45$, $5\times9 = 45$)
• Common factors: $1, 3, 9$

Step4: Solve for 9 and 10

• Factors of 9: $1, 3, 9$ ( $1\times9 = 9$, $3\times3 = 9$)
• Factors of 10: $1, 2, 5, 10$ ( $1\times10 = 10$, $2\times5 = 10$)
• Common factor: $1$

Answer:

1. Common factors of 15 and 18: \(1, 3\)
2. Common factors of 36 and 45: \(1, 3, 9\)
3. Common factor of 9 and 10: \(1\)