Uses of Prime Factor Decomposition Flashcards

All 5 cards in this deck

How can you tell from its prime factorisation that a number is a square number?

Every prime appears to an even power.
e.g. $900 = 2^2 \times 3^2 \times 5^2$

How can you tell from its prime factorisation that a number is a cube number?

Every index is a multiple of 3.
e.g. $216 = 2^3 \times 3^3$

What are the steps to find the smallest integer to multiply a number by to make a square number?
e.g. 40

1. Write it as a product of prime powers: $40 = 2^3 \times 5$.
2. Pick out the primes with odd indices: $2$ and $5$.
3. Multiply those primes together: multiply 40 by $2 \times 5 = 10$.

How do you find the square root of a number from its prime factorisation?
e.g. $2^4 \times 3^2$

Halve each index.
$\sqrt{2^4 \times 3^2} = 2^2 \times 3 = 12$

True or false? A number whose prime factorisation contains a prime raised to an odd power cannot be a square number.

True. A square number has every prime to an even power.