Factors of 6 | Factor Tree of 6 - Explained Simply

Today we are going to present here Factor Tree of 6. The factor is the number that divides the original number. The factors of 6 are 1, 2, 3 and 6 itself.

What are the factors of 6?

We want to find all the whole numbers that can divide 6 without leaving any remainder.

Factor Tree Method of 6: Explained Simply

Imagine you have 6 cookies and you want to share them equally among a group of friends.

If you have 1 friend, that friend gets 6 cookies (6 ÷ 1 = 6).

If you have 2 friends, each friend gets 3 cookies (6 ÷ 2 = 3).

If you have 3 friends, each friend gets 2 cookies (6 ÷ 3 = 2).

If you have 6 friends, each friend gets 1 cookie (6 ÷ 6 = 1).

In this scenario, the number of friends (1, 2, 3, 6) are the factors of 6, because they allow for an equal, whole-number division of the cookies.

Factors of 6: Explained Simply

Using the Division Test for 6:

Is 1 a factor of 6?

6 ÷ 1 = 6 (No remainder). Yes, 1 is a factor. (Its pair is 6).

Is 2 a factor of 6?

6 ÷ 2 = 3 (No remainder). Yes, 2 is a factor. (Its pair is 3).

Is 3 a factor of 6?

6 ÷ 3 = 2 (No remainder). Yes, 3 is a factor. (Its pair is 2).

N.B. we've already found 2 as a factor, so 3 is its pair.

Is 4 a factor of 6?

6 ÷ 4 = 1 with a remainder of 2. No, 4 is not a factor.

Is 5 a factor of 6?

6 ÷ 5 = 1 with a remainder of 1. No, 5 is not a factor.

Is 6 a factor of 6?

6 ÷ 6 = 1 (No remainder). Yes, 6 is a factor. (Its pair is 1). We've gone through all possibilities and confirmed our initial pairs.

Using Multiplication Pairs for 6:

1 × 6 = 6 (So, 1 and 6 are factors)

2 × 3 = 6 (So, 2 and 3 are factors)

If we tried 3 × ?, we'd get 3 × 2 = 6, which is just the reverse of 2 × 3. We've found all the unique pairs!

Based on both methods, we can definitively list the factors of 6. It's good practice to list them in ascending order: 1, 2, 3, 6.

Properties of 6

6 is not a prime number.
6 is a composite number.
6 is a positive integer. (1+2+3=6)
6 is the smallest perfect number. (The next one is 28)

Prime Factorization of 6

There are a couple of straightforward methods to find the prime factors of 6. We'll explore two popular ones:

The Factor Tree Method
The Division Method

The Factor Tree Method

The factor tree method is a visual way to break down a number. Find any two factors of 6 (other than 1 and 6). The most obvious pair is 2 and 3. Draw branches down from 6 to these two factors.

/ \

2 3

Is 2 a prime number?

Yes. Circle it or mark it.

Is 3 a prime number?

Yes. Circle it or mark it.

/ \

② ③

(Circles indicate prime numbers)

Therefore, the circled numbers are your prime factors of 6.

The Division Method

The division method involves repeatedly dividing the number by the smallest possible prime factor until you can no longer divide.

Divide by the smallest prime number that divides 6 evenly.

The smallest prime number is 2. Does 2 divide 6 evenly? Yes, 6 ÷ 2 = 3.

Write the prime factor (2) on the left and the result (3) below the original number.

2|6

Take the new result (3) and repeat the process:

Is 3 a prime number? Yes.

Can 3 be divided by any prime numbers other than itself and 1? No.

Stop when the number at the bottom is a prime number.

2 | 6

3 | 3

1 (We divide by 3 to show it's a prime factor, resulting in 1)

The prime factors are the numbers on the left side of the division bars: 2 and 3.

Conclusion

No matter which method you use, the result is the same:

The prime factorization of 6 is 2 × 3.

This means that if you multiply the prime numbers 2 and 3 together, you will get the number 6. These are the fundamental prime building blocks of 6.