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  1. Glossary
  2. /Mathematics
  3. /Prime Factorisation

What is Prime Factorisation?

In short

Prime factorisation is writing a number as a product of prime numbers. By the fundamental theorem of arithmetic, this can be done in only one way, apart from the order.

In simple words

A prime number has exactly two factors, 111 and itself. To factorise, divide by the smallest prime that goes in, repeatedly. Prime factorisation is the key to finding the HCF and the LCM. Write each number as a product of primes. The HCF takes the smaller power of each common prime, and the LCM takes the larger power of every prime that appears.

Example

132=22×3×11132 = 2^2 \times 3 \times 11132=22×3×11 and 198=2×32×11198 = 2 \times 3^2 \times 11198=2×32×11. The HCF is 2×3×11=662 \times 3 \times 11 = 662×3×11=66 and the LCM is 22×32×11=3962^2 \times 3^2 \times 11 = 39622×32×11=396.

Also searched as: prime factorization of 9, hcf of 132 and 198, hcf.

Learn it properly

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Related terms

  • Quadratic Equation
  • Real Numbers

← All glossary terms

Learn it in

  1. Rational and Irrational NumbersClass 9 to 10
  2. Irrational Numbers and ProofsClass 9 to 10
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Practise

  1. Write the integers from 1 to 60 one after another to make the single large number N =…Advanced
  2. A square garden has an area of 18 m². Find its side, its perimeter and its diagonal…Medium
  3. Find √3 + √5 to three decimal places. Prove that √3 + √5 is irrational…
Hard
  • Find the whole number m for which (3 + √m)(3 - √m) = 4…Medium
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    Quick questions

    1. Below are four claims: two are about a linear equation in integers and two are about…Advanced
    2. A prime p is called a ladder prime when all five numbers p, p + 6, p + 12, p + 18 and p…Hard
    3. Four students each state a rule about irrational numbers. Whose rule is wrong?Medium

    More Mathematics terms

    1. Algebraic Identity
    2. Arithmetic Progression
    3. Complex Number
    4. Derivative
    5. Function
    6. Isosceles Triangle
    All Mathematics terms →

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