Find Prime Factorization/Factors Of 6 - Cuemath

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Factors of 6 are the list of integers that can be evenly divided into 6. There are overall 4 factors of 6 i.e. 1, 2, 3 and 6 where 6 is the biggest factor. The sum of all factors of 6 is 12. Its Prime Factors are 1, 2, 3, 6 and (1, 6) and (2, 3) are Pair Factors.

• Factors of 6: 1, 2, 3 and 6
• Negative Factors of 6: -1, -2, -3 and -6
• Prime Factors of 6: 2, 3
• Prime Factorization of 6: 2 × 3 = 2 × 3
• Sum of Factors of 6: 12

1.	What Are the Factors of 6?
2.	Important Notes
3.	How to Calculate the Factors of 6?
4.	Factors of 6 by Prime Factorization
5.	Factors of 6 in Pairs

What Are the Factors of 6?

Factors of 6 are those numbers that divide it completely and give the remainder as 0.

For example, 6 ÷ 1

We get 6 as the quotient and 0 as the remainder. This means that 6 is divisible by 1.

Similarly, 6 ÷ 2 = 3, 6 ÷ 3 = 2, 6 ÷ 6 = 1

Thus, the possible factors of 6 are 1, 2, 3, and 6.

Important Notes

• Factors of 6 are 1, 2, 3, and 6.
• 1 is a universal factor. It is a factor of all numbers.
• The number itself is a factor of the number as it divides itself exactly.
• The factors of 6 in pairs are (2, 3), (3, 2), (6, 1), and (1, 6).
• 2 and 3 are the prime factors of 6.

How to Calculate the Factors of 6?

In prime factorization, we express 6 as the product of its prime factors and in the division method, we see what numbers divide 6 exactly without leaving a remainder.

6 is a composite number and it should have prime factors. Here, we will first use the division method to find the factors of 6.

The first step is to divide the number 6 with the smallest prime factor, say 2, and so on.  

The division shows that the number 6 is exactly divisible by 1, 2, 3, and 6.

Hence, the factors of 6 by division method are 1, 2, 3, and 6.

Thus, all numbers which leave a remainder 0 are the factors of 6. We see that 1, 2, 3, and 6 are the factors of 6.

Explore factors using illustrations and interactive examples: 

• Factors of 5 - The factors of 5 are 1 and 5.
• Factors of 7 - The factors of 7 are 1 and 7.
• Factors of 8 - The factors of 8 are 1, 2, 4, and 8.
• Factors of 9 - The factors of 9 are 1, 2, 3, and 9.
• Factors of 10 - The factors of 10 are 1, 2, 5, and 10.

Factors of 6 by Prime Factorization Method

The prime factors of 6 can be represented by the factor tree method as:

    

The prime factors of 6 can be represented by the upside-down division method as:

The factors of 6 by the prime factorization method are 1, 2, 3, and 6.

Here, 2 and 3 are the prime factors of 6.

Factors of 6 in Pairs

To find the factors of 6 in pairs, multiply the two numbers in a pair to get the resultant number as 6. 

If 1 × 6 = 6, then (1, 6) is a pair factor of 6.

Similarly, let us find other pairs.

2 × 3 = 6, 3 × 2 = 6, and 6 × 1 = 6.

Therefore, the pair factors are (2, 3), (3, 2), (6, 1), and (1, 6).

There are negative factor pairs of 6 as well. Those pairs also give 6 as the result when they are multiplied. 

Thus, (-2, -3), (-3, -2), (-1, -6), and (-6, -1) are negative pair factors of 6.

 

Solved Examples

1. Example 1 what are the negative pair factors of 6?

   Solution:

   To find the negative pair factors, proceed with the following steps:

   -2 × -3 = 6, -3 × -2 = 6, -6 × -1 = 6, -1 × -6 = 6.

   Therefore, the negative pair factors are (-2, -3) and (-6, -1) without considering the order of multiplication.

2. Example 2 Help Andy list the prime factors of 6.

   Solution:

   The factors of 6 by the prime factorization method are 1, 2, 3, and 6.

   A prime number does not have any other factor other than 1 and itself. Hence, the prime factors of 6 are 2 and 3.

    

3. Example 3: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 6 and 6.

   Solution:

   The factors of 6 are 1, 2, 3, 6 and factors of 6 are 1, 2, 3, 6. Therefore, the Lowest Common Multiple (LCM) of 6 and 6 is 6 and Highest Common Factor (HCF) of 6 and 6 is 6.

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FAQs on Factors of 6

What are the Factors of 6?

The factors of 6 are 1, 2, 3, 6 and its negative factors are -1, -2, -3, -6.

How Many Factors of 6 are also Factors of 3?

Since, the factors of 6 are 1, 2, 3, 6 and the factors of 3 are 1, 3. Hence, [1, 3] are the common factors of 6 and 3.

What Numbers are the Prime Factors of 6?

The prime factors of 6 are 2, 3.

What is the Sum of the Factors of 6?

All the Factors of 6 are 1, 2, 3, 6 and therefore the sum of all these factors is 1 + 2 + 3 + 6 = 12

What is the Greatest Common Factor of 6 and 3?

The factors of 6 and 3 are 1, 2, 3, 6 and 1, 3 respectively. Common factors of 6 and 3 are [1, 3]. Hence, the Greatest Common Factor (GCF) of 6 and 3 is 3.

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