Factors of 8 | Factor Tree of 8 - Explained Simply

Today we are going to present here Factor Tree of 8. The factor is the number that divides the original number. The factors of 8 are 1, 2, 4 and 8 itself.

What are the factors of 8?

We want to find all the whole numbers that can divide 8 without leaving any remainder.

Factor Tree Method of 8: Explained Simply

One of the most straightforward ways to find the factors of a number is by systematically testing numbers through division. We'll start with 1 and work our way up to the number itself, checking if each number divides 8 evenly.

Division Pairs of 8

Here's how we find the factors of 8 using division:

Step 1: Start with 1.

Is 8 divisible by 1?

Yes, 8 ÷ 1 = 8.

1 and 8 are factors of 8.

Step 2: Move to 2.

Is 8 divisible by 2?

Yes, 8 ÷ 2 = 4.

2 and 4 are factors of 8.

Step 3: Move to 3.

Is 8 divisible by 3?

No, 8 ÷ 3 = 2 with a remainder of 2.

3 is not a factor of 8.

Step 4: Move to 4.

Is 8 divisible by 4?

Yes, 8 ÷ 4 = 2.

Note: We've already found 2 and 4 in Step 2. This shows that factors often appear in pairs. Once you reach a number whose "partner" (the result of the division) is already in your list, you can usually stop.

Step 5: Move to 5, 6, 7.

None of these divide 8 evenly (8 ÷ 5 = 1 R 3; 8 ÷ 6 = 1 R 2; 8 ÷ 7 = 1 R 1).

Step 6: Move to 8.

Is 8 divisible by 8?

Yes, 8 ÷ 8 = 1.

We've already identified 8 and 1.

By systematically going through these steps, we've identified all the positive integer factors of 8.

Multiplication Pairs of 8

Another excellent way to find factors is by thinking about which pairs of numbers multiply together to give you the target number. This method naturally reveals the factor pairs.

Let's find the factors of 8 using multiplication pairs:

Pair 1: What two numbers can we multiply to get 8, starting with 1?

1 × 8 = 8

Factors: 1 and 8

Pair 2: What's the next smallest whole number we can try? 2.

2 × 4 = 8

Factors: 2 and 4

Pair 3: What's the next number? 3. Does 3 multiply by a whole number to get 8?

No. (3 × 2 = 6, 3 × 3 = 9).

Stopping Point: The next number to try would be 4. But we've already found 4 in the pair (2 × 4). Once you reach a factor that you've already listed as part of a pair (or its partner), you know you've found all the unique pairs.

This method confirms the factors we found through division.

The Positive Integer Factors of 8 are 1, 2, 4 and 8.

Prime Factorization of 8

A prime number is a whole number greater than 1 that has exactly two distinct positive factors: 1 and itself.

A composite number is a whole number greater than 1 that has more than two distinct positive factors.

Now, let's apply these concepts to our target number: 8.

First, let's identify if 8 is prime or composite.

Factors of 8 are 1, 2, 4, 8.

Since 8 has more than two factors (1 and itself), 8 is a composite number. This means we can perform prime factorization on it.

Is 8 prime number?

We can use a couple of common methods to find the prime factors of 8:

The Division Method

This method involves repeatedly dividing the number by the smallest possible prime number until you reach 1.

Start with the number 8.

Find the smallest prime number that divides 8 evenly.

The smallest prime number is 2.

Is 8 divisible by 2?

Yes, 8 ÷ 2 = 4.

Now take the result (4) and repeat the process.

Is 4 divisible by 2?

Yes, 4 ÷ 2 = 2.

Take the new result (2) and repeat again.

Is 2 divisible by 2?

Yes, 2 ÷ 2 = 1.

Stop when you reach 1.

The prime factors are all the prime numbers you used for division.

For 8, these were 2, 2, and 2.

Therefore, the prime factorization of 8 is: 2 × 2 × 2

This can also be written in exponential form: 2³ (read as "2 to the power of 3" or "2 cubed").

The Factor Tree Method

The factor tree method provides a visual way to break down a number into its prime factors.

Start with the number 8 at the top.

Find any two factors of 8 (other than 1 and 8).

We can choose 2 and 4. Draw branches from 8 to 2 and 4.

/ \

2 4

Circle any factors that are prime numbers.

2 is a prime number, so circle it.

/ \

(2) 4

Continue breaking down any composite numbers until all branches end in prime numbers.

4 is a composite number. Break it down into its factors: 2 and 2. Draw branches from 4 to 2 and 2.

/ \

(2) 4

/ \

(2) (2)

Circle these new prime factors.

Now all the "leaves" of our tree are prime numbers.

The prime factors are all the circled numbers at the ends of the branches.

For 8, these are 2, 2 and 2.

Therefore, the prime factorization of 8 is 2 × 2 × 2. Or in exponential form: 2³. This means that the number 8 is simply made up of three '2's multiplied together.