Question 13 of 18intermediate🔧 ApplyNumerical4 marks

Find the common factors and the HCF of the following numbers: (a) 50, 60 (b) 140, 275 (c) 77, 725 (d) 370, 592

(a)

Find common factors and HCF of 50 and 60

Answer

Common factors: 1, 2, 5, 10. HCF = 10.

(b)

Find common factors and HCF of 140 and 275

Answer

Common factors: 1, 5. HCF = 5.

(c)

Find common factors and HCF of 77 and 725

Answer

Common factors: 1. HCF = 1.

(d)

Find common factors and HCF of 370 and 592

Answer

Common factors: 1, 2, 37, 74. HCF = 74.

Explanation

(a) 50 = 2×52 \times 5², 60 = 2² × 3×53 \times 5. Common subparts: 1, 2, 5, 2×52 \times 5=10. (b) 140 = 2² × 5×75 \times 7, 275 = 5² × 11. Only common prime is 5. HCF = 5. (c) 77 = 7×117 \times 11, 725 = 5² × 29. No common primes. HCF = 1. (d) 370 = 2×52 \times 5 × 37, 592 = 2⁴ × 37. Common subparts: 1, 2, 37, 2×372 \times 37=74.

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