Factors of 12

Factors of 12 are those numbers that divide 12 completely without leaving any remainder. There are 6 factors of 12 among which 12 is the biggest factor and 2 and 3 are its prime factors. The prime factorization of 12 can be done by multiplying all its prime factors such that the product is 12. Let us learn about all the factors of 12, the prime factorization of 12, the factor pairs of 12, and the factor tree of 12 in this article.

There are 6 factors of 12 that can be listed as 1, 2, 3, 4, 6, and 12. It means that 12 is completely divisible by all these numbers. Apart from these, 12 also has negative factors that can be listed as, -1, -2, -3, -4, -6, and -12. For negative factors, we need to multiply a negative factor by a negative factor, like, (-6) × (-2) = 12.

How to Find the Factors of 12?

Factorization of a number means writing the number as a product of its factors. The most commonly used method to find the factors of a number is using the multiplication method. Let us find all the factors of 12 using multiplication.

All Factors of 12 using Multiplication

Let us find the factors of 12 using the multiplication method with the help of the following steps.

• Step 1: In order to find the factors of 12 using multiplication, we need to check what pairs of numbers multiply to get 12. So, we need to divide 12 by natural numbers starting from 1 and go on till 9. We need to make a note of those numbers that divide 12 completely.
• Step 2: The numbers that completely divide 12 are known as its factors. We write that particular number along with its pair and make a list as shown in the figure given above. As we check and list all the numbers up to 9, we automatically get the other pair factor along with it. For example, starting from 1, we write 1 × 12 = 12, and 2 × 6 = 12, and so on. Here, (1, 12) forms the first pair, (2, 6) forms the second pair and the list goes on as shown. So, as we write 1 as the factor of 12, we get the other factor as 12; and as we write 2 as the factor of 12, we get 6 as the other factor. Like this, we get all the factors.
• Step 3: After the list is noted, we get all the factors of 12 starting from 1 up there, coming down and then we go up again up to 12. This gives us a complete list of all the factors of 12 as shown in the figure given above.

Therefore, the factors of 12 can be listed as 1, 2, 3, 4, 6, and 12. Now, let us learn about the prime factorization of 12.

Prime Factors of 12

The prime factors of 12 are those factors of 12 that are prime numbers. The prime factors of 12 are different from the factors of 12. As we saw in the section above, the factors of 12 can be listed as 1, 2, 3, 4, 6, and 12. However, all of these are not prime numbers. So, let us find the prime factors of 12 using prime factorization in the following section.

Prime factorization is a way of expressing a number as a product of its prime factors. The prime factors of a number are those factors that are prime numbers. The prime factorization of 12 can be done using the following steps. Observe the figure given below to understand the prime factorization of 12.

• Step 1: The first step is to divide the number 12 with its smallest prime factor. We know that a prime factor is a prime number which is a factor of the given number. In this case, it is 2. So, 12 ÷ 2 = 6
• Step 2: We need to repeatedly divide the quotient by 2 until we get a number that is no more divisible by 2. So, we divide 6 again by 2 which is 6 ÷ 2 = 3. After this, we divide 3 by 3 to get 1 as the quotient,
• Step 3: Now, we need not proceed further as we have obtained 1 as our quotient.
• Step 4: Therefore, the prime factorization of 12 is expressed as 2 × 2 × 3 = 2² × 3; where 2 and 3 are prime numbers and the prime factors of 12.

We can also find the prime factors of 12 using a factor tree. The factor tree of 12 can be drawn by factorizing 12 until we reach its prime factors. These factors are split and written in the form of the branches of a tree. The final factors are circled and are considered to be the prime factors of the 12. Let us find the prime factors of 12 using the following steps and the factor tree given below.

• Step 1: Split 12 into two factors. Let us take 2 and 6.
• Step 2: Observe these factors to see if they are prime or not.
• Step 3: Since 2 is a prime number we circle it as one of the prime factors of 12. We move on to 6, which is a composite number and further split it into more factors. In other words, we repeat the process of factorizing 6 and splitting it into branches until we reach a prime number. So, we split 6 into 2 and 3.
• Step 4: At this stage, we are left with prime numbers, 2 and 3. We circle them since we know that they cannot be factorized further. This is the end of the factor tree.
• Step 5: Therefore, the prime factors of 12 = 2 × 2 × 3

Note: It should be noted that there can be different factor trees of 12. For example, we can start by splitting 12 into 3 and 4. Here, 3 is already a prime factor and 4 can be split further into 2 and 2. Finally, we can observe the same prime factors, that is, 12 = 2 × 2 × 3

The factors of 12 can be written in pairs. This means that the product of the pair factors of 12 is always 12. The factors of 12 in pairs can be written as shown in the table given below:

It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number. Let us have a look at the negative pair factors of 12.

The following points explain some features of the pair factors of 12.

• The pair factors of the number 12 are whole numbers in pairs that are multiplied to get the original number, i.e., 12.
• Pair factors could be either positive or negative but they cannot be fractions or decimal numbers.
• The positive pair factors of 12 are as follows: (1, 12), (2, 6), (3, 4). The negative pair factors of 12 are (-1, -12), (-2, -6), (-3, -4)

Important Notes

• Only composite numbers can have more than two factors. Since 12 is a composite number, it has more than two factors.
• Every factor of a given number is either less than or equal to the given number.
• The number of factors of a given number is finite. 12 has 6 factors.
• Factors of 12 are those numbers that divide 12 completely without leaving any remainder.
• 12 has a total of 6 factors: 1, 2, 3, 4, 6, and 12.
• There is a trick to calculate the total number of factors of a number. For example, 12 = 2 × 2 × 3 = 2² × 3. We get the prime factorization of 12 as 2² × 3. Just add one (1) to the exponents 2 and 1 individually and multiply their sums. (2 + 1) × (1 + 1) = 3 × 2 = 6. This means 12 has 6 factors in all.

Points to remember

Let us recollect the list of the factors, the negative factors, and the prime factors of 12.

• Factors of 12: 1, 2, 3, 4, 6 and 12
• Negative Factors of 12: -1, -2, -3, -4, -6 and -12
• Prime Factors of 12: 2, 3
• Prime Factorization of 12: 2 × 2 × 3 = 2² × 3

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What are all the Factors of 12?

The factors of 12 are 1, 2, 3, 4, 6, 12 and its negative factors are -1, -2, -3, -4, -6, -12.

What are the Prime Factors of 12?

There are two prime factors of 12, and they are 2 and 3. The prime factors of a number are those factors that are prime numbers. In this case, if we do the prime factorization of 12, we get 2 × 2 × 3 = 2² × 3, where 2 and 3 are prime numbers and the prime factors of 12.

What are the Common Factors of 12 and 18?

The factors of 12 can be listed as 1, 2, 3, 4, 6, and 12 and the factors of 18 can be listed as 1, 2, 3, 6, 9, 18. Among these, we can list the common factors of 12 and 18 as 1, 2, 3, and 6. Now, we can find the Greatest Common Factor (GCF) of 12 and 18 which is 6.

What is the Sum of all the Factors of 12?

All the factors of 12 are 1, 2, 3, 4, 6, 12. Therefore, the sum of all these factors is 1 + 2 + 3 + 4 + 6 + 12 = 28.

What is the Greatest Common Factor of 12 and 8?

The factors of 12 and 8 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 8 respectively. The common factors of 12 and 8 are (1, 2, 4). Hence, the Greatest Common Factor (GCF) of 12 and 8 is 4.

How Many Factors of 8 are also Common to the Factors of 12?

Since, the factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 8 are 1, 2, 4, 8. Hence, (1, 2, 4) are the common factors of 12 and 8.

What are the Prime Divisors of 12?

The prime divisors of 12 are the prime factors of 12 that are 2 and 3. The prime divisors are known as the prime factors. These are factors that are prime numbers. In this case, after we do the prime factorization of 12, we get 2 × 2 × 3 = 2² × 3, where 2 and 3 are prime numbers. Therefore, the prime divisors or prime factors of 12 are 2 and 3.