Question

If prime factors of 288 can be expressed as 3p ×2q then find the values of p and q

Answer 1

GivEn:

• Prime factors of 288 can be expressed as 3ᵖ × 2ᑫ.

To find:

• The values of p and q.

Solution:

⌬ 288 this number is being expressed as 3ᵖ × 2ᑫ

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« Now, By using prime factorisation method,

⇏288 = 2 × 2 × 2 × 2 × 2 × 3 × 3

[ Refer attachment ]

As we see that,

• There are 5 2's & 2 3's

∴ Thus, The values of p & q are 2 & 5.

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« Now, Let's verify,

⇏ 288 = 3ᵖ × 2ᑫ

Putting the values of p & q,

⇏ 288 = 3² × 2⁵

⇏ 288 = 288

∴ Hence, Verified !

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⠀⠀⠀⠀⠀⠀⠀⌬ Additional information :

• Prime factorisation is a method of finding prime factors of a number.

• Prime factors are the factors obtained by prime factorisation.

• Prime numbers are those numbers which do not have any factors.