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

What is the value of log₃(27)?

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

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What is the sum of all odd numbers from 1 to 99?

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If the radius of a circle is 7 cm, what is its circumference?

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

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The probability of getting an even number when rolling a die is:

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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What is the cube root of 729?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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