Prime Time - Prime Factorisation

Find the prime factorisation of $72$ using the Division Method.

$\begin{array}{r|l} 2 & 72 \\ \hline 2 & 36 \\ \hline 2 & 18 \\ \hline 3 & 9 \\ \hline 3 & 3 \\ \hline & 1 \end{array}$ Prime factors of $72 = 2 \times 2 \times 2 \times 3 \times 3$

We start dividing $72$ by the smallest prime number, $2$. We continue dividing the resulting quotients by prime numbers ($2, 2, 2, 3, 3$) until we reach $1$. The product of these divisors gives the prime factorisation.

Express $48$ as a product of its prime factors using the Factor Tree Method.

Step 1: $48 = 2 \times 24$ Step 2: $24 = 2 \times 12$ Step 3: $12 = 2 \times 6$ Step 4: $6 = 2 \times 3$ Final prime factorisation: $48 = 2 \times 2 \times 2 \times 2 \times 3$

In the Factor Tree, we branch out $48$ into $2$ and $24$. $2$ is prime, so we circle it. We then branch $24$ into $2$ and $12$, and so on, until only prime numbers ($2, 2, 2, 2, 3$) remain at the ends of the branches.

Find the prime factorisation of the smallest $3$-digit number.

The smallest $3$-digit number is $100$. $\begin{array}{r|l} 2 & 100 \\ \hline 2 & 50 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \end{array}$ $100 = 2 \times 2 \times 5 \times 5$

The smallest $3$-digit number is $100$. We perform prime factorisation by dividing by $2$, then $2$ again, then $5$, and finally $5$ to reach $1$.