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Question

How many factors of 2⁷ × 3³ × 5⁴ × 7 are even numbers?

This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper PDF (31-Jan-2021) (Shift 1)
The correct answer is

280

280 is correct.

A factor is even only if it contains at least one 2. So the power of 2 can be chosen from 1 to 7 (7 ways), the power of 3 from 0 to 3 (4 ways), the power of 5 from 0 to 4 (5 ways) and the power of 7 from 0 to 1 (2 ways).

Even factors = \(7 \times 4 \times 5 \times 2 = 280\)

Check: total factors = \(8 \times 4 \times 5 \times 2 = 320\) and odd factors = \(4 \times 5 \times 2 = 40\), and \(320 - 40 = 280\).

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