Prime Factor Decomposition Flashcards

All 6 cards in this deck

What does it mean to write a number as a product of its prime factors?

Writing it as a multiplication in which every factor is prime.
e.g. $60 = 2 \times 2 \times 3 \times 5$

What are the steps of the factor tree method for prime factorisation?
e.g. 36

1. Split the number into any factor pair: $36 = 4 \times 9$.
2. Keep splitting any non-prime branch: $4 = 2 \times 2$, $9 = 3 \times 3$.
3. Multiply all the circled primes: $36 = 2^2 \times 3^2$.

What are the steps of the repeated division method for prime factorisation?
e.g. 90

1. Divide by the smallest prime that goes in: $90 \div 2 = 45$.
2. Repeat on each answer: $45 \div 3 = 15$, $15 \div 3 = 5$, $5 \div 5 = 1$.
3. Multiply the divisors used: $90 = 2 \times 3^2 \times 5$.

How do you write a prime factorisation in index (product) notation?
e.g. $2 \times 2 \times 2 \times 7$

Collect repeated primes as powers, writing primes in increasing order: $2^3 \times 7$.

What does the unique factorisation theorem state?

Every integer greater than 1 can be written as a product of primes in exactly one way (apart from the order of the factors).

True or false? Starting a factor tree for 36 with $4 \times 9$ instead of $6 \times 6$ gives a different prime factorisation.

False. Any correct starting pair leads to the same set of primes, $2^2 \times 3^2$.