Using a factor tree find all prime factors of 128

Using a factor tree find all prime factors of 128

The Correct Answer and Explanation is:

To find all the prime factors of 128 using a factor tree, we can follow these steps:

Step 1: Start with 128

The first step is to start with the number 128 and break it down into smaller factors. We know that 128 is an even number, so it’s divisible by 2 (the smallest prime number).

128÷2=64128 ÷ 2 = 64128÷2=64

Step 2: Continue factoring 64

Now we have 64. Since 64 is also even, we can divide it by 2.

64÷2=3264 ÷ 2 = 3264÷2=32

Step 3: Continue factoring 32

We continue with 32, which is also even. Dividing by 2 again gives us:

32÷2=1632 ÷ 2 = 1632÷2=16

Step 4: Continue factoring 16

Now we have 16, and since it’s even, we divide it by 2 again:

16÷2=816 ÷ 2 = 816÷2=8

Step 5: Continue factoring 8

We keep going with 8, which is also divisible by 2:

8÷2=48 ÷ 2 = 48÷2=4

Step 6: Continue factoring 4

We now have 4, and since it’s even, we divide by 2 once again:

4÷2=24 ÷ 2 = 24÷2=2

Step 7: Final factor

At this point, we are left with 2, which is a prime number, and we stop here.

Step 8: Prime factorization of 128

The factor tree is now complete. We can express the prime factorization of 128 as follows:

128=2×2×2×2×2×2×2128 = 2 × 2 × 2 × 2 × 2 × 2 × 2128=2×2×2×2×2×2×2

This can be written in exponential form as:

128=27128 = 2^7128=27

Explanation:

• We started with the number 128 and repeatedly divided it by 2, the smallest prime factor, until we reached 2 itself, which is a prime number.
• Each division showed that 128 can be broken down into the prime factor 2, repeated 7 times.
• Thus, the prime factorization of 128 is 272^727, meaning 128 is the product of seven 2s.