Question 4 of 18intermediate🔧 ApplyNumerical5 marks

Find the HCF of the following numbers: (a) 24, 180 (b) 42, 75, 24 (c) 240, 378 (d) 400, 2500 (e) 300, 800

(a)

Find HCF of 24 and 180

Answer

HCF = 12

(b)

Find HCF of 42, 75, and 24

Answer

HCF = 3

(c)

Find HCF of 240 and 378

Answer

HCF = 6

(d)

Find HCF of 400 and 2500

Answer

HCF = 100

(e)

Find HCF of 300 and 800

Answer

HCF = 100

Explanation

(a) 24 = 2³ × 3, 180 = 2² × 3² × 5. Common: 2² × 3 = 12. (b) 42 = 2×32 \times 3 × 7, 75 = 3×53 \times 5², 24 = 2³ × 3. Only common prime is 3 (minimum 1 occurrence). (c) 240 = 2⁴ × 3×53 \times 5, 378 = 2×32 \times 3³ × 7. Common: 2×32 \times 3 = 6. (d) 400 = 2⁴ × 5², 2500 = 2² × 5⁴. Common: 2² × 5² = 100. (e) 300 = 2² × 3×53 \times 5², 800 = 2⁵ × 5². Common: 2² × 5² = 100.

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