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Factors of 2:Prime Factorization, Methods, Tree, and Examples

Factors of 2 is a term that refers to the numbers that, when multiplied together, produce a result of 2, or the numbers by which 2 may be entirely divided. As a result, if a number divides 2 with 0 being the remainder, it is referred to as a factor.

Only the number two is an even prime. It is the unique number that, when added to itself and multiplied by itself, yields the same answer, i.e., 4. All the even numbers are multiples of two, as you will discover in this article. 

Factors of two can have both positive and negative values. Moreover, an essential detail regarding factors is that two is the factor of all numbers. A number’s factors can be found using either division or multiplication.

Fortunately, there are numerous approaches to finding integer factors. Even easier methods exist for determining a number’s factors. Divide the number by itself until the remainder equals zero, at which time you consider the quotient and divisor factors of the given number.

In this article, you will be guided about all the details related to the factors of 2. To gain a more thorough understanding, we will discuss the prime factors of 2,  factors pairs of 2, effortless solutions, and fun facts about the number 2.

What Are the Factors of 2?

The factors of number 2 are 1 and 2 as the number 2 is a prime number.

The factor pairings of 2 are (1, 2) and (2, 1). To do this, pair the integers together so that the outcome is 2. Furthermore, we are aware that the actual divisors of the number 2 are its factors.

How To Calculate the Factors of 2?

To calculate the factors of 2, division and multiplication are the two main methods used. To determine the factors, let’s first discuss how to divide.

In the beginning, list all the numbers below 2. Next, multiply each number by 2. The divisions of 2 with a remainder of 0 are referred to as its factors.

Let’s look at the following example for a clearer understanding:

2 can be divided by 1, the smallest factor of all the numbers. Therefore, 2 and 1 are the factors of 2.

\[ \frac{2}{1} = 2 \]

This proves that quotient and divisor (1, 2) are the factors of 2 because the quotient is a full integer with no remainder.

Let’s start focusing on multiplying to find the factors of 2. Consider 2 as the sum of two whole numbers in all probable situations. All the integers in each of these products are factors of 2. Take a look at these examples:

1 x 2 = 2

2x 1 = 2

 Hence, the factors are 1 and 2.

Factors of 2 by Prime Factorization 

One method for expressing a specific number as the product of its prime factors is the prime factorization method, which involves figuring out which prime factors can combine to form the product of the number.

In plainer terms, it is a method for figuring out or showing an integer as the sum of prime integers.

The prime factorization of the number 2 is 2. Only the even prime number 2 exists. There are just two factors of 2, 1, and 2. As a result, we cannot factor it further because the factor of every number will be lower than or equal to that number.

Here is a diagram showing how 2 is divided into its prime factors:

Figure 1

Factor Tree of 2

Although a number’s factors can be expressed in many different ways, one of the many ways to graphically display a number’s prime factors is by using a “Factor tree.” The real number serves as the root of the factor tree, from which branches extend up to the prime number. Therefore, it is a factor.

Let’s look at the factor tree of 2 in diagram form:

Figure 2

Therefore according to prime factorization, 1 and 2 are regarded as the prime factors of 2. Here are some fascinating details related to the number 2:

  1. If an integer is divisible by 2, it is nevertheless referred to as an even number. Moreover, as 2 is the smallest prime number, it is also known as the oddest prime.
  2. Only the numbers 2 and 3 are consecutive prime numbers. Furthermore, the square of two was the first irrational number ever discovered.
  3. The first Sophie Germain prime, the first Lucas prime, and the first factorial prime are all 2. Additionally, 2 is the first magic number.
  4. In the Fibonacci sequence, the number two is also the third or fourth number.
  5. Helium is a chemical element with a two-atomic mass.
  6. The name of the second asteroid ever found is 2 Pallas.
  7. The total number of polynucleotide strands in a DNA double helix is 2. 
  8. 2 is the number of points scored during an American football safety.
  9. Basketball players receive 2 points for each field goal within the three-point line.
  10. A shooting guard is a two in basketball. Other than this, in baseball, position number two is that of the catcher.
  11. 2 was used as a shortcut for the reduplication in Indonesian and Malay spelling before 1972.
  12. A stellar system called a binary star comprises two stars that revolve around their mass centers.

Factor of 2 in Pairs 

Two integers are referred to as a Factor Pair when they are paired to produce the number itself as the result of their multiplication. These are the positive factor pairs of 2:

1 x 2 = 2, (1, 2) is a pair factor of 2.

2 x 1 = 2, (2, 1) is a pair factor of 2.

The fact that any two negative numbers can be multiplied together to produce a positive number makes it possible for negative pair factors as well. Changing the signs makes it possible to recognize the negative factor pair. Following are the negative factor pairs:

-1 x -2 = 2, (-1, -2) is a pair factor of 2.

-2 x -1 = 2, (-2, -1) is a pair factor of 2.

Thus, given above are the factor pairs of 2.

Factors of 2 Solved Examples

Here are some wonderful and entertaining examples to assist you in understanding factors even better!

Example 1:

The factors of 10 are known to Alicia, but she is not familiar with the factors of 2. She received a worksheet with factor-related questions as a part of her assignment. One of the questions is, “What are the common factors between 2 and 10?” 

Discover the factors of 2 to help Alicia. Additionally, assist her in determining the common factors between 2 and 10.

Solution

To solve the question in the worksheet, Alicia needs to find out the factors of 2. She will have to multiply all the numbers below 2. 1 is the only number below 2, so:

1 x 2 = 2

Henceforth, Factors of 2 are 1 and 2.

On the other hand, the Factors of 10 are 1, 2, 5, and 10.

Thus, the common factors between 2 and 10 are 1 and 2.

Example 2

Jimmy was asked on his final exam, “Is two a prime number or a composite number?” Jimmy studied for the exam, but he had no idea how to answer this question. Assist Jimmy in identifying whether 2 is a composite number or a prime number.

Solution

Determining the factors of 2 first is the simple way to find the answer to this problem.

There are two factors of 2: 1 and 2.

The whole number is greater than 1 with only itself, and the number 1 as the factor is referred to as a prime number.

Any number with more than two factors is known as a  composite number.

Therefore, in the light of the above statements, the number 2 is a prime number because it only has two factors.

Example 3

On his smartphone, Howl was playing a general knowledge game. He solved all the questions to go to the next level of the game, except for one. He was stuck on the last question, which was to identify the factors of 2 from a list of random numbers. 

The numbers were as follows:

3, 1, 5, 2, 10, 8, 4, 6

The options Howl got were:

  1. 4, 8 and 6
  2. 1, 3 and 5
  3. 1 and 2
  4. 1, 2, 4, 6, 8 and 10

Howl needs your assistance finding the correct answer to advance to the next level.

Solution

To figure out the factors of two, multiply all the numbers below two.

1 x 2 = 2

Hence, 2 has only two factors (as it is a prime number) which are 1 and 2. Therefore, this shows that Howl will choose option 3 as the correct answer.

All the images/diagrams are created using GeoGebra.

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