Both 59 and 67 are prime numbers. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

Factor Tree for 59 and 67:

Since 59 and 67 are prime numbers, their factor trees are very simple:

• 59:

  • The only factors of 59 are 1 and 59 itself.
  • The factor tree of 59 would just be the number 59.

     59
    /  \
   1    59
  

• 67:

  • The only factors of 67 are 1 and 67 itself.
  • The factor tree of 67 would just be the number 67.

     67
    /  \
   1    67
  

Conclusion:

• Prime Factorization of 59: $59$ (itself)
• Prime Factorization of 67: $67$ (itself)

Since they are already prime, there's no further breakdown possible using the factor tree method.

Do you have any other numbers in mind or need further explanation?

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Here are 8 related questions that might expand your understanding:

1. How do you check if a number is prime?
2. What is the factor tree for the number 91?
3. Can composite numbers have multiple factor trees?
4. How can you use prime factorization to find the greatest common divisor (GCD) of two numbers?
5. What is the prime factorization of 100 using the factor tree method?
6. Why are prime numbers important in number theory?
7. How do you use prime factorization to solve problems involving LCM (Least Common Multiple)?
8. What are the properties of prime numbers?

Tip: When working with larger numbers, start by checking divisibility with smaller primes (like 2, 3, 5) to see if they are prime or composite.