What are the prime factors of 18 by using the factor tree method and division method?

The prime factors of 18 are 2 and 3. Here's how to find them using the factor tree method and the division method:

1. Factor Tree Method

• Start with the number 18.
• Find any two factors of 18. For example, 2 and 9.
• Write these factors as branches of the tree.
• If a factor is prime, circle it. If a factor is composite (not prime), find two factors of that number and continue branching.
• Continue until all branches end in prime numbers.

Here's the factor tree for 18:

      18
     /  \
    2    9
        / \
       3   3

The prime factors are the numbers at the end of the branches that are circled: 2, 3, and 3. Therefore, the prime factors of 18 are 2 and 3. The prime factorization is 2 x 3 x 3, or 2 x 3².

2. Division Method

• Start with the number 18.
• Divide 18 by the smallest prime number that divides it evenly (which is 2).
• Write the prime number (2) and the result of the division (9).
• Continue dividing the result by the smallest prime number that divides it evenly.
• Repeat until you reach 1.

Here's the division method for 18:

18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

The prime factors are the prime numbers you used to divide: 2, 3, and 3. Therefore, the prime factors of 18 are 2 and 3. The prime factorization is 2 x 3 x 3, or 2 x 3².