Factors of 6

Factors of 6 are 1, 2, 3 and 6. The integers that can divide the number evenly are known as the factor of that number. When 6 is divided by their factor then the remainder must be zero and the quotient is a factor of 6. There are four factors of 6 which are 1, 2, 3, and 6. Hence, the smallest factor is 1 and the greatest factor is 6 itself.

In this article, we will answer different questions related to factors like What is factor, Factors of 6 along with Prime Factorization and Factor Tree of 6.

What is a Factor?

Factors are defined as numbers which when multiplied together gives back the original number. Every number has atleast two factors. Each factor when divided by the given number returns 0 as a remainder.

A factor is a number which completely divides the given number i.e. it divides the number without leaving any remainder.

Factor of the number have its own pair. If you multiplied pairs, you get your original number. Every pair of factors divides the original number completely. Examples of Factors are:

• Factor of 18: 1, 2, 3, 6, 9, 18.
• Factors of 20: 1, 2, 4, 5, 10, 20.

Important Points:

• Every number has 1 and number itself as its factor.
• The smallest factor of any number is always 1.
• The highest Factor of any number is always the number itself.

Read More, Factors of a Number

What are Factors of 6?

Factors of 6 are those number which divides 6 completely. Also 1 and 6 are the permanent factor of 6. So, for the number 6, {1, 2, 3, 6} are the factors. These number exactly divides 6.

Let’s understand this from a table:

Factors of 6	Division	Remainder
1	6 ÷ 1	0
2	6 ÷ 2	0
3	6 ÷ 3	0
6	6 ÷ 6	0

In the above table, we can see that all the factors exactly divides 6 and leaves the remainder 0.

All Factors of 6

Here is a list for all the factors of 6

Factors of 6 are 1, 2, 3 and 6.

Prime Factor of 6

Prime factors are those factors of a number which are prime and completely divisible by the original number. Prime factors when multiplied together gives back the original number.

The Prime factor of the number 6 are 2 and 3.

But we express it in given form:

Prime Factor of 6 are: 2 and 3 which are expressed as 2¹ × 3¹= 6.

How to Find Factors of 6?

To find the factors of 6, we need to find out all the whole numbers that can divide 6 without leaving a remainder.

Here are steps we can follow:

• Start from 1 till 6 and check if the number can divide 6 without leaving any reminder.

• If yes, then note down both the number and the result when 6 is divided by it.

• Else, check for next number and repeat it till number reaches 6.

• List all the Factors and the resulting list is 1, 2, 3 and 6.

Divisor	Is the number a factor of 6?	Pair
1	We know that 1 is a factor of every number	1 × 6 = 6
2	6 is divisible by 2	2 × 3 = 6
3	6 is divisible by 3	3 × 2 = 6
4	6 is not divisible by 4	–
5	6 is not divisible by 5	–
6	6 is also divisible by 6	6 × 1 = 6

Hence, the list of all factors of 6 is 1, 2, 3, 6.

Prime Factorization of 6

Prime factorization is method of expressing any number as the product of its prime factors. To find out prime factorization of 6, divide 6 by its prime factors (you can begin by dividing by its smallest factor that is 2), until we get the quotient as 1.

To find the prime factorization of 6, follow the given steps:

• Step 1: Choose smallest prime number(which is 2 here) which can perfectly divide 6.
• Step 2: Divide 6 with the chosen number and note the result(3) and factor which is 2.
• Step 3: Repeat again same steps until the quotient turns to 1.
• Step 4: List all the numbers together to get all the prime factors of 6.

So, prime factorization of 6 = 2 × 3 = 2¹ × 3¹.

This process of prime factorization can be illustrated as follows:

Read More, Prime Factorization.

Factor Tree of 6

A factor tree is a diagram that is used to express all the prime factors of a number in the form of a tree diagram. In the factor tree method, we start dividing a number and continue the division process until prime numbers appear at all the leaf nodes. The prime numbers at each leaf node are the prime factors of that number.

Here’s a factor tree for the number 6:

Factor Pairs of 6

Factor Pairs of 6 are pairs of numbers that gives 6 by multiplying two factors such as (1 , 6). We consider all integers when forming factor pairs, including two negative numbers. If, upon multiplying these numbers, we obtain 6, it is also included in the factor pairs. Factor pairs can be positive as well as negative.

Below is a table illustrating positive and negative factor pairs of 6:

Positive Factor Pairs of 6	Negative Factor Pairs of 6
(1 , 6)	(-1 , -6)
(2 , 3)	(-2 , -3)

Factors of 6 Solved Examples

Example 1: What is the sum of all the factors of 6?

Solution:

Factors of 6 are 1, 2, 3 and 6

Sum of the factors of 6 = (1 + 2 + 3 + 6)

Sum of the factors of 6 = 12

Example 2: What are common factors of 6 and 12.

Solution:

Factors of 6 are {1, 3, 6}

Factors of 12 are {1, 2, 3, 6, 12}

Hence, the common factors of 6 and 12 are {1, 2, 3, 6}

Example 3: What is the sum of odd factors of 6.

Solution:

Odd factors of 6 are 1, 3.Sum = 1 + 3 = 4

Example 4: What is the prime factorization of 6?

Solution:

Prime factorization of 6 is 2 × 3 or 2¹ × 3¹

Example 5: What are the negative pair factors of 6?

Solution:

Negative pair factors of 6 are {-1, -6} and {-2, -3}.

Factors of 6 – Practice Questions

Q1: How many factors does 6 have?

Q2: Determine the product of all the factors of 6.

Q3: Is 6 itself a factor of 6?

Q4: Is 1 a factor of 6?

Q5: If you group the factors of 6 into pairs that multiply to 6, what are the pairs?

Q6: Are there more even or odd factors of 6? List them.

Read More,

• Factors of 36
• Factors of 12
• Factors of 96

Factor of 6: Frequently Asked Questions

What are Factors of 6?

Factors of 18 are: 1, 2, 3 and 6.

How many Factors does 6 have?

The number 6 has exactly 4 Factors.

Is 3 a Factor of 6?

Yes, 3 is the factor of 6 as 3 completely divides 6.

Is 5 a Factor of 6?

No , 5 is not a factor of 6.

What is the Highest Common Factor (HCF) of 6 and 12?

Factors of 6: {1, 2, 3, 6}Factors of 12: {1, 2, 3, 4, 6, 12}The highest common factor (HCF) of 6 and 12 is 6.

What is Least Common Factor (LCM) of 6 and 9?

To find LCM, we need to find multiples of 6 and 9:

Multiples of 6: 6, 12, 18, 24, 90,…..

Multiples of 9: 9, 18, 27, 36, …….The least common multiple is 18