Question 1 of 18intermediate🔧 ApplyNumerical5 marks

List all the factors of the following numbers: (a) 90 (b) 105 (c) 132 (d) 360 (this number has 24 factors) (e) 840 (this number has 32 factors)

(a)

List all factors of 90

Answer

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

(b)

List all factors of 105

Answer

1, 3, 5, 7, 15, 21, 35, 105

(c)

List all factors of 132

Answer

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

(d)

List all factors of 360

Answer

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

(e)

List all factors of 840

Answer

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840

Explanation

(a) 90 = 2×32 \times 3 × 3×53 \times 5. All subparts give 12 factors. (b) 105 = 3×53 \times 5 × 7. All subparts give 8 factors. (c) 132 = 2×22 \times 2 × 3×113 \times 11. All subparts give 12 factors. (d) 360 = 2³ × 3² × 5. All subparts give 24 factors. (e) 840 = 2³ × 3×53 \times 5 × 7. All subparts give 32 factors.

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