Topic Details (Notes format)

How to Perform Prime Factorization

Subject: Mathematics

Book: Maths Mastery

Prime factorization is the process of breaking a number down into the product of its prime factors. For example, 60 can be factorized as 2 × 2 × 3 × 5, or 2² × 3 × 5. Common methods include repeatedly dividing by the smallest prime until the result is 1. Prime factorization underpins concepts like Greatest Common Divisor (GCD) and Least Common Multiple (LCM). It is extremely useful in simplifying fractions, analyzing cryptographic algorithms, and understanding integer properties. Regular practice with small to large numbers strengthens your factoring agility and cements foundational number theory skills.

Practice Questions

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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A car travels 240 km in 4 hours. What is its average speed?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If the radius of a circle is doubled, what happens to its area?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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