Find the prime factorisation of 676.

Step-by-step solution

1. 1

   Divide by the smallest prime repeatedly. $676$ is even, so start with $2$:

   $676\div 2=338$

   $338$ is still even, so divide again:

   $338\div 2=169$

2. 2

   Stop dividing by 2 and move up the primes. $169$ is odd, so $2$ is exhausted. It is not divisible by $3$ (digit sum $16$), not by $5$ (last digit $9$), not by $7$ ($7\times 24=168$, remainder $1$), and not by $11$ ($11\times 15=165$, remainder $4$).

3. 3

   Try $13$.

   $169\div 13=13$

   and $13$ is prime, so the division tree terminates. Note we only had to test primes up to $\sqrt{169}=13$.

4. 4

   Collect the factors with exponents.

   $676=2\times 2\times 13\times 13=2^2\times 13^2$

5. 5

   Observe that every exponent is even, so 676 is a perfect square. Halving the exponents gives the root:

   $\sqrt{676}=2\times 13=26$

   Check: $26^2=676$ $\checkmark$, and $2^2\times 13^2=4\times 169=676$ $\checkmark$.