Find the common factors of the following pairs of numbers. (a) 12 and 16 (b) 8 and 12 (c) 4 and 16 (d) 2 and 9 (e) 3 and 5 (f) 12 and 15 (g) 20 and 5 (h) 9 and 21 (i) 6 and 27
(a) 12 and 16: Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 ∴ Common factors are 1, 2, 4.
(b) 8 and 12: Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 ∴ Common factors are 1, 2, 4.
(c) 4 and 16: Factors of 4: 1, 2, 4 Factors of 16: 1, 2, 4, 8, 16 ∴ Common factors are 1, 2, 4.
(d) 2 and 9: Factors of 2: 1, 2 Factors of 9: 1, 3, 9 ∴ Common factor is 1 only.
(e) 3 and 5: Factors of 3: 1, 3 Factors of 5: 1, 5 ∴ Common factor is 1 only (both are prime).
(f) 12 and 15: Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15 ∴ Common factors are 1, 3.
(g) 20 and 5: Factors of 20: 1, 2, 4, 5, 10, 20 Factors of 5: 1, 5 ∴ Common factors are 1, 5.
(h) 9 and 21: Factors of 9: 1, 3, 9 Factors of 21: 1, 3, 7, 21 ∴ Common factors are 1, 3.
(i) 6 and 27: Factors of 6: 1, 2, 3, 6 Factors of 27: 1, 3, 9, 27 ∴ Common factors are 1, 3.
Explanation
To find common factors, list all factors of each number and identify which appear in both lists. Factors of 12: 1,2,3,4,6,12. Factors of 16: 1,2,4,8,16. Common: 1,2,4. Similarly for other pairs.
Solution Steps
(a) Factors of 12: 1,2,3,4,6,12. Factors of 16: 1,2,4,8,16. Common: 1,2,4
(b) Factors of 8: 1,2,4,8. Factors of 12: 1,2,3,4,6,12. Common: 1,2,4
(c) Factors of 4: 1,2,4. Factors of 16: 1,2,4,8,16. Common: 1,2,4
(d) Factors of 2: 1,2. Factors of 9: 1,3,9. Common: 1 only
(e) Factors of 3: 1,3. Factors of 5: 1,5. Common: 1 only (both are prime)
(f) Factors of 12: 1,2,3,4,6,12. Factors of 15: 1,3,5,15. Common: 1,3
(g) Factors of 20: 1,2,4,5,10,20. Factors of 5: 1,5. Common: 1,5
(h) Factors of 9: 1,3,9. Factors of 21: 1,3,7,21. Common: 1,3
(i) Factors of 6: 1,2,3,6. Factors of 27: 1,3,9,27. Common: 1,3