Factors of 2 | Prime Factorization of 2 | Factor Tree of 2

Factors of 2: The numbers that are completely divisible by 2 without leaving any remainder are the numbers known as factors of 2. In other words, if two numbers are multiplied and their result comes out to be 2, those numbers are factors of 2. Since 2 is a prime number, it has only two factors, with 2 being the highest factor of the number 2.

In this article, we will discuss the factors of 2, how to find them, prime factorization, and the factor tree of 2, along with some solved examples.

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What Are the Factors of 2?

The factors of 2 can be defined as the numbers which are completely divisible by the number 2, or you can define it as two numbers that, when multiplied by each other, give the result of 2.  The factors of 2 can be listed as 1 and 2. The factors of 2 have both a positive pair and a negative one. For the negative pair of factors of 2, we need to multiply two negative numbers, i.e., (-2) X (-1) =2.  

Factors of 2 = 1, 2

Positive Factors of 2 in Pairs

The positive factor pairs of 2 are (1, 2).

Negative Factors of 2 in Pairs

The negative factor pairs of 2 is (-1, -2).

How to Find the Factors of 2?

To find factors of 2, we need to determine if the given number is a prime number or not. If the given number is a prime number, then it has only two factors: the original number and 1.

If the given number is a composite number, then it has more than two factors. Here, the given number is 2. As a result, the factors of 2 are 2, 1.

To cross-check, we can find factors of 2 using the long division method. The steps to finding factors of 2 using the long division method are explained below.

Step 1: Divide the number 2 by the sequence of natural numbers. Those numbers which are completely divisible by the number 23 and leave no remainder are the numbers known as factors of 2.

Step 2: Since 1 and 2 are the only numbers that are divisible by 2, the factors of 2 are 1 and 2.

• 2/1 = 2 (Remainder = 0)
• 2/2 = 1 (Remainder = 1)

Prime Factors of 2

We can find the prime factors of 2 through prime factorization. Let us see the steps below for the prime factorization of 2:

Step 1: To find the prime factors of 2, using the prime factorization method, we can write the prime factors of 2 as 2 = 1 X 2.
Step 2: Now that 2 is a prime number, we cannot factor it further because prime numbers do not have factors other than 1 and the number itself.
Step 3: Therefore, the prime factor of 2 is 2 itself.

What Is the Factor Tree of 2?

We can also find the prime factors of the number 2 using the factor tree method. The steps to finding prime factors of number 2 using the factor tree method are given below:

• Step 1: Place the number 2 at the top of the factor tree and keep splitting until we are left with prime numbers at the end.
• Step 2: Now, as the tree branches, we will write down the pair factors of 2. Here we are using the pair factor 1, 2, as the first branch of 2.
• Step 3: Because 1 and 2 are prime numbers that cannot be divided further, they are the end of the tree branch. 

The factor tree of 2 is given below:

Solved Examples

1. How to determine whether 2 is a prime number or a composite number.
First of all, we will have to find out all the factors of 2.
The only factors of 2 are 1 and 2.
A number is said to be “prime” if it has just two factors.
On the other hand, a number is considered composite if it has more than two factors.
Therefore, since 2 has only two factors, we can state that it is a prime number.

2. How to determine the prime factors of 12?
We can calculate all the factors of 12 using prime factorization.
12 can be prime factorized as 2 x 2 x 3.
Prime factors of 12 are 2 and 3, and we see that 2 is a repeated factor.

3. Find the common factors of 4 and 8?
Factors of 4 are 2 and 1.
Factors of 8 are 2 and 1.
So, the common factor of 4 and 8 is 2. Hence, 2 is the only common factor of 4 and 8. 

4. Help Adam determine the number which when multiplied by -23 gives 23.
The negative factor pair of 23 is (-1,-23)
Therefore when -23 is multiplied by -1, the product is 23.
-23 x -1 = 23

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Frequently Asked Questions

What is a factor pair of 2?
Each factor pair consists of two factors that, when multiplied together, produce a specific product. Thus the factor pair of 2 consists of two numbers which when multiplied give out 2, these are (1, 2) or (2, 1).

Whether 2 is a factor of every number, just like 1?
No, unlike 1, 2 is not the factor of every number. Since it is the factor of only even numbers and not odd ones.

What are the multiples of 2?
The numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, etc. are all multiples of 2.

What are the factors of a number?
Factors are the numbers that when multiplied together yield any different number. The term “factor” refers to a number’s exact divisors, and every number has at least two factors.

Identify the two factors of 12.
The formula for factoring 12 into its prime factors is 12 = 2 × 2 × 3
As a result, 12 has only two prime factors, 2 and 3.