MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 26(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section C, question 26(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(b) · 3 marks · Short answerReal Numbers

The factor tree of a number x is shown below. Find the values of x, y, a and b. Hence, write the product of the prime factors of the number x so obtained.

Figure in the paper: Factor tree: top box x splits into 2 and y. y splits into 2 and 210. 210 splits into a and 70. 70 splits into 2 and 35. 35 splits into 5 and b. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Each box equals the product of the two boxes directly below it.

Hint 2

Start at the bottom (35) and work up to x. Then collect all the prime leaves of the tree.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$35 = 5 \times b \Rightarrow b = 7$
½ mark
$210 = a \times 70 \Rightarrow a = 3$
½ mark
$y = 2 \times 210 = 420$
½ mark
$x = 2 \times y = 2 \times 420 = 840$
½ mark
Product of prime factors: $840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7 = 2^{3} \times 3 \times 5 \times 7$
1 mark

Answer: b = 7, a = 3, y = 420, x = 840; 840 = 2³ × 3 × 5 × 7

Where the marks are

Finds $b = 7$ (½ mark)
Finds $a = 3$ (½ mark)
Finds $y = 420$ (½ mark)
Finds $x = 840$ (½ mark)
Writes $840 = 2^{3} \times 3 \times 5 \times 7$ (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2025: question 26(b)

Hints

Step-by-step solution

Revise the chapter

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