Find the prime factors of 340 using a factor tree

General
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find the prime factors of 340 using a factor tree

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Find the prime factors of 340 using a factor tree

Answer:

To find the prime factors of 340 using a factor tree, we will systematically break down the number into its prime factors. A factor tree is a helpful visual aid that shows how a number can be divided into its prime factors. Here’s how you can do it:

  1. Start with the number 340.

    We are going to repeatedly divide it by the smallest prime numbers (2, 3, 5, etc.) until we reach only prime numbers.

  2. Divide by 2 (because 340 is even):

    $$ 340 \div 2 = 170 $$

    So, one of the factors is 2. You can start the factor tree by splitting 340 into 2 and 170.

      340
  /  \
 2   170

  3. Continue with 170:

    170 is also an even number, so divide by 2 again.

    $$ 170 \div 2 = 85 $$

    Your factor tree now adds another branch.

      340
  /  \
 2   170
    /  \
   2   85

  4. Factor 85:

    85 is not divisible by 2 since it’s odd, so try the next smallest prime number, which is 3. Check divisibility by adding the digits of 85 (8 + 5 = 13) which is not divisible by 3. So, we try the next prime number, which is 5.

    Since 85 ends in 5, it is divisible by 5.

    $$ 85 \div 5 = 17 $$

    Now your factor tree looks like this:

      340
  /  \
 2   170
    /  \
   2   85
      /  \
     5   17

  5. Verify if 17 is a prime number:

    17 is a prime number, as it is only divisible by 1 and itself.

    Now that you cannot factor the numbers further, your complete factor tree is:

      340
  /  \
 2   170
    /  \
   2   85
      /  \
     5   17

  6. List the prime factors:

    The prime factors of 340 are 2, 2, 5, and 17. Combining these, the prime factorization of 340 is:

    $$ 340 = 2^2 \times 5 \times 17 $$

Summary:

The prime factorization of 340 can be determined using a factor tree, splitting it step-by-step into the prime factors: 2, 5, and 17. This method allows for a clear visual representation of how a composite number breaks down into prime numbers.