 # Factors of 3

The factors of 3 are the numbers that divide 3 evenly without leaving any remainder. As we know that the number 3 is the first odd prime number. The factors and the pair factors of 3 can be expressed in positive and negative forms. For example, the pair factor of 3 is represented by (1, 3) or (-1, -3). If we multiply -1 and -3, it will result in the number 3. In this article, we will learn the factors of 3, pair factors of 3 and the prime factors of 3 using the prime factorization method and many solved examples.

## What are the Factors of 3?

The numbers that divide 3 exactly and leave a remainder value as 0 are the factors of 3. As the number 3 is the first odd prime number, it has only two factors, such as one and the number itself. Therefore, the factors of 3 are 1 and 3. Similarly, the negative factors of 3 are -1 and -3.

 Factors of 3: 1 and 3. Prime Factorization of 3: 1 × 3.

## Pair Factors of 3

The numbers that are multiplied together in pairs resulting in the number 3 is a pair factor of 3. Since the number 3 is a prime number, it should have one positive pair factor and one negative pair factor. The following are the positive and negative pair factors of 3:

Positive Pair Factors of 3:

 Positive Factors of 3 Positive Pair Factors of 3 1 × 3 (1, 3)

Negative Pair Factors of 3:

 Negative Factors of 3 Negative Pair Factors of 3 -1 × -3 (-1, -3)

Therefore, the positive and negative pair factors of 3 are (1, 3) and (-1, -3) respectively.

## Factors of 3 by Division Method

In the division method, the factors of 3 are found by dividing the number 3 by the integer numbers. If the integer divides 3 exactly, then the integer is a factor of 3. Now, divide the number 3 by 1 and then continue with the numbers 2 and 3.

• 3/1 = 3 (Factor is 1 and Remainder is 0)
• 3/3 = 1 (Factor is 3 and Remainder is 0)

If 3 is divisible by 2, it leaves a remainder value as 1 and hence, 2 is not a factor of 3.

Therefore, the factors of 3 are 1 and 3.

## Prime Factorization of 3

The process of writing the number 3 as the product of its prime factors is the prime factorization of 3. Go through the following procedure to find the prime factors of 3 using the prime factorization method.

Consider a pair factor of 3, say (1, 3)

Here, the number 3 is a prime number, so we cannot be able to split further.

Thus, 3 is written as 1 × 3.

Therefore, the prime factorization of 3 is 1 × 3 or 3.

Note: If a number in the pair factor is composite, split the composite number into its prime factors, and write the numbers in the form of the product of its prime factors.

## Video Lesson on Prime Factors More on Factors of a Number: Factors of 5 Factors of 12 Factors of 13 Factors of 31

### Solved Examples

Example 1:

Find the common factor of 3 and 2.

Solution:

The factors of 3 are 1 and 3.

The factors of 2 are 1 and 2.

As both the numbers 2 and 3 are prime numbers, the common factor of 3 and 2 is 1.

Example 2:

Find the common factor of 3 and 4.

Solution:

Factors of 3 = 1 and 3.

Factors of 4 = 1, 2 and 4.

Hence, the common factor of 3 and 4 is 1.

Example 3:

What are the common factors of 3 and 6?

Solution:

The factors of 3 are 1 and 3.

The factors of 6 are 1, 2, 3 and 6.

Therefore, the common factors of 3 and 6 are 1 and 3.

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## Frequently Asked Questions on Factors of 3

Q1

### What are the factors of 3?

As the number 3 is a prime number, it has only two factors, such as 1 and 3.

Q2

### What is the prime factorization of 3?

The prime factorization of 3 is 1 × 3.

Q3

### What are the positive and negative pair factors of 3?

The positive and negative pair factors of 3 are (1, 3) and (-1, -3), respectively.

Q4

### Is 2 a factor of 3?

No, 2 is not a factor of 3. If 3 is divided by 2, it leaves a remainder of 1, and hence, 2 is not a factor of 3.

Q5

### What is the sum of factors of 3?

The sum of factors of 3 is 4. We know that the factors of 3 are 1 and 3.
Hence, the sum of factors of 3 = 1+3 = 4.