If you expand the prime factorisation, you get :

2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 7 × 7 × 11


Now these are all the copies of the prime factors this number has.

Any factor of this number can have a mixture of copies of these prime factors.

Recall that prime factors are the simplest and cannot be broken down anymore.


So just pick some prime factors from the above , such that you get a product which is above 100.

For example,

2⁴ × 3⁵ × 7² × 11

If I were to pick two 7s and two 2 s, I can rewrite it as :

(2² × 3⁵ × 11) × 2² × 7²

= (2² × 3⁵ × 11) × 4 × 49

= (2² × 3⁵ × 11) × 196


So my factor is 196 and the number is a multiple of 196 and (2² × 3⁵ × 11)

This question is open ended so there many possible correct answers.


The important thing is to know what the index notation stands for.

① aⁿ = a × a × a × a .... (there are n copies of a)

Eg.

2⁴ = 2 × 2 × 2 × 2 (4 copies of 2)


② aⁿ⁺ᵐ = aⁿ × aᵐ

Eg.

2⁴
= 2³⁺¹
= 2³ × 2¹
= (2 × 2 × 2) × (2)
= 2 × 2 × 2 × 2


③ aⁿ⁻ᵐ = aⁿ ÷ aᵐ = aⁿ/aᵐ


Eg.

3⁵
= 3⁷⁻²
= 3⁷/3²
= (3×3×3×3×3×3×3)/(3×3)
= 3×3×3×3×3

I understand it now, thank you!!