I need to find the prime factors of $5! + 6!$ and then pick the largest one. I know that $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$ and $6! = 6 \times 5! = 6 \times 120 = 720$. So $5! + 6! = 120 + 720 = 840$. I could try to divide 840 by different prime numbers, starting from the smallest ones, until I get a quotient of 1. Alternatively, I could use prime factorization trees to find the prime factors of 840. I think the second method might be faster and more systematic, so I'll try that. I start by dividing 840 by 2, the smallest prime number, and I get 420. I divide 420 by 2 again and get 210. I divide 210 by 2 once more and get 105. I can't divide 105 by 2 anymore, so I move on to the next prime number, 3. I divide 105 by 3 and get 35. I divide 35 by 5, another prime number, and get 7. 7 is already a prime number, so I can stop here. The prime factors of 840 are 2, 2, 2, 3, 5, and 7. The largest one is 7, so that's my answer. 
What is the largest prime factor of $5! + 6!$?