Edit: I did the inverse with 3307 and it was doing so good but then completely fumbled at the end lmao

To determine whether 3307 is a composite number, we need to check if it can be divided by any integer other than 1 and itself. If it can be divided by any other integer, it is composite.

Let’s check if 3307 is divisible by any prime numbers up to its approximate square root (around 57.5).

• 3307 is odd, so it is not divisible by 2.
• The sum of its digits is 13, which is not divisible by 3.
• It does not end in 0 or 5, so it is not divisible by 5.
• Dividing by 7: (3307 \div 7 = 472.42857), not an integer.
• Dividing by 11: Alternating sum of digits: (3 - 3 + 0 - 7 = -7), not divisible by 11.
• Dividing by 13: (3307 \div 13 = 254.3846), not an integer.
• Dividing by 17: (3307 \div 17 = 194.5294), not an integer.
• Dividing by 19: (3307 \div 19 = 174.0526), not an integer.
• Dividing by 23: (3307 \div 23 = 143.7826), not an integer.
• Dividing by 29: (3307 \div 29 = 114.0345), not an integer.
• Dividing by 31: (3307 \div 31 = 106.6774), not an integer.
• Dividing by 37: (3307 \div 37 = 89.3784), not an integer.
• Dividing by 41: (3307 \div 41 = 80.6585), not an integer.
• Dividing by 43: (3307 \div 43 = 76.9069), not an integer.
• Dividing by 47: (3307 \div 47 = 70.3617), not an integer.
• Dividing by 53: (3307 \div 53 = 62.3962), not an integer.

Now let’s check division by 7 again more carefully: [ 3307 \div 7 = 472.428571 ]

So far so good

This calculation was correct initially, confirming it’s not divisible by 7. But there’s another calculation involving 47 that needs rechecking: [ 3307 \div 47 = 70.3617 ]

Uhh ok I guess.

This means 3307 is not evenly divisible by 47 either.

However, let’s check another prime factor: 53. [ 3307 \div 53 = 62.3962 ]

…right

Rechecking again for any missed divisor, we finally find: [ 3307 = 53 \times 59 ]

Hence, 3307 is divisible by 53 and 59, proving it’s composite since it has divisors other than 1 and itself.

WTF