Question 25 of 36intermediate🔧 ApplyNumerical3 marks

Find the prime factorisation of these numbers without multiplying first a. 56×2556 \times 25 b. 108×75108 \times 75 c. 1000×811000 \times 81

(a)

Find the prime factorisation of 56×2556 \times 25 without multiplying first.

Answer

56×2556 \times 25 = 2³ × 7×57 \times 5²

(b)

Find the prime factorisation of 108×75108 \times 75 without multiplying first.

Answer

108×75108 \times 75 = 2² × 3⁴ × 5²

(c)

Find the prime factorisation of 1000×811000 \times 81 without multiplying first.

Answer

1000×811000 \times 81 = 2³ × 3⁴ × 5³

Explanation

(a) 56 = 2³ × 7 and 25 = 5². Combining: 56×2556 \times 25 = 2³ × 7×57 \times 5². (b) 108 = 2² × 3³ and 75 = 3×53 \times 5². Combining: 108×75108 \times 75 = 2² × 3³ × 3×53 \times 5² = 2² × 3⁴ × 5². (c) 1000 = 2³ × 5³ and 81 = 3⁴. Combining: 1000×811000 \times 81 = 2³ × 5³ × 3⁴.

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