Find the largest prime factor of $9879$.
We see that

$$9879=10000-121=100^2-11^2$$Thus,

$$9879=(100-11)(100+11)=89(111)=3*37*89$$So the answer is $\boxed{89}$.
89
Level 4
Algebra
Problem: Find the largest prime factor of $9879$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the largest prime factor of 9879, first, we need to determine if 9879 is divisible by smaller prime numbers. We start by checking divisibility by 2, the smallest prime. Since 9879 is odd, it is not divisible by 2. Next, we check divisibility by 3 by summing the digits: 9 + 8 + 7 + 9 = 33, which is divisible by 3. Thus, we divide 9879 by 3, yielding 3293.

Now, we need to factor 3293. We check for divisibility by the next few primes: 5 (not applicable as it does not end in 0 or 5), 7 (3293 ÷ 7 = 470.4286, not an integer), and 11 (3293 ÷ 11 = 299.3636, not an integer). Continuing this process, we check 13, 17, 19, and so on, until we reach 29, which also does not divide evenly.

Next, we check 37. Dividing 3293 by 37 gives us 89, which is a prime number. At this point, we have factored 9879 into 3, 37, and 89. To find the largest prime factor, we compare these factors: 3, 37, and 89. The largest of these is 89. Therefore, the final answer is 89.<|END_OF_LATENT|> The final answer is $89$.