Question

Find all the prime factors of $1729$ and arrange them in ascending order. Also, state the relation, if any, between two consecutive prime factors.

Answer 1

Step 1: Find the prime factors and arrange in ascending order.

On the prime factorization of $1729$, we get the factors as

So, the prime factorization of $1729$ is $7\times 13\times 19$

Hence, the prime factors of $1729$ is $7,13$ and $19$.

Now, arranging the factors in ascending order, we get, $7<13<19$.

Step 2: State the relation between two constructive prime factors.

The difference between these prime factors.

$$\begin{gathered} 19–13=6 \\ 13–7=6 \end{gathered}$$

So, there is a difference of $6$ between two constructive prime factors or we can say they form a arithmetic progression.

Hence, the prime factors of $\mathbf{1729}$ is $\mathbf{7}\mathbf{,}\mathbf{}\mathbf{13}$ and $\mathbf{19}$, written in ascending order and there is a difference of $6$ between the two constructive prime factors.