1. **State the problem:** Factorise fully the expression $6 + 36x$. 2. **Identify common factors:** Look for the greatest common factor (GCF) of the terms $6$ and $36x$. 3. **Calculate the GCF:** The GCF of $6$ and $36x$ is $6$ because $6$ divides both terms. 4. **Factor out the GCF:** Write the expression as $6(1 + 6x)$. 5. **Check the factorisation:** Multiply back to verify: $6 \times 1 + 6 \times 6x = 6 + 36x$. 6. **Final answer:** The fully factorised form is $$6(1 + 6x)$$.