Factors of 3 | How to Find the Prime Factors of 3 by the Prime Factorization Method? (2024)

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.

Table of Contents:

• What Are The Factors Of 3?
• Pair Factors Of 3
• Factors Of 3 By Division Method
• Prime Factorization Of 3
• Solved Examples
• FAQs

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.

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:

Negative Pair Factors of 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

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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