Factors
Change SetupFactors
Official curriculum roadmap, subject/topic distribution, negative marking rules, pacing guidelines, and solved sample questions.
🎯 Mapped Subjects & Topic Question Distribution
💡 Strategic Preparation & Exam Hall Guidelines
To maximize your score on Factors, candidates are advised to follow a structured three-pass approach. In the First Pass, solve all direct recall and formula-based questions within 30 seconds each to secure foundational marks. In the Second Pass, tackle multi-step analytical and quantitative reasoning problems. In the Third Pass, review marked questions and verify calculations.
Practice with the interactive player below to evaluate your speed and accuracy under real exam pressure. Every question features full mathematical formulas, step-by-step worked solutions, and conceptual explanations vetted by Apex Rankers Academy subject matter specialists.
📝 Pre-Rendered Solved Sample Questions & Detailed Solutions
Review the solved problems below to understand question phrasing, answer choices, and step-by-step solution logic prior to starting the full interactive practice drill:
\(2100=21\times 100=(3\times 7)\times (2^{2}\times 5^{2})=2^{2}\times 3^{1}\times 5^{2}\times 7^{1}\)
Make it a perfect square:
For a number to be a perfect square, all the exponents in its prime factorization must be even numbers.
\(2^{2}\) and \(5^{2}\) already have even exponents.
\(3^{1}\) and \(7^{1}\) have odd exponents, so we must multiply by another 3 and 7 to make them even (\(3^{2}\) and \(7^{2}\)).
Calculate the least square number:
Multiply 2100 by the missing factors (\(3 \times 7 = 21\)):
\(2100\times 21=\mathbf{44100}\)
(Verification: \(\sqrt{44100} = 210\), which is a perfect integer).