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Real Numbers
RD Sharma
CBSE
Grade 10

Question:

The prime factorisation of $3825$ is:
(a) $3 \times 5^2 \times 17$
(b) $3^2 \times 5^2 \times 17$
(c) $3^3 \times 5 \times 17$
(d) $3^2 \times 5^3 \times 17$

Step-by-Step Solution

Key Concept: Divide continuously by prime factors: $3825 = 9 \times 25 \times 17 = 3^2 \times 5^2 \times 17$.
$3825 / 3 = 1275 / 3 = 425 / 5 = 85 / 5 = 17 / 17 = 1$. [0.5 Mark]
$3825 = 3^2 \times 5^2 \times 17$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Prime factorisation steps: 0.5 Mark
Selecting correct canonical form: 0.5 Mark

Correct Answer: $3^2 \times 5^2 \times 17$
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