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Factors

Factors of 12 | How To Find Prime Factors of 12?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 12 | How To Find Prime Factors of 12?

Factors of 12 | How To Find Prime Factors of 12?

Factors of 12: The numbers which divide the number (12) evenly without leaving any remainder are known as factors of 12. The factors of 12 can either be negative or positive. Let’s learn how to find factors of 12 using various methods in this article, as well as prime factors of 12. Scroll down to learn more.

What Are the Factors of 12?

Since 12 is a composite number, the number 12 has more than two factors. There are a total of 6 factors for the number 12, which doesn’t leave any remainder after division. Hence, 12 has six factors.

Factors of 12: 1, 2, 3, 4, 6, and 12.
Negative Factors of 12-1,-2,-3, -4, and -12.
Prime Factorization of 12: 2 X 2 X 3 or 22 X 3
Prime Factors of 12: 2, 3
Sum of Factors of 128: 28
Sum of Prime Factors of 12: 5

Factors of 12 in Pairs

When we multiply one pair of factors, which gives the actual number, it is known as pair factors of 12. For example, to get the number 12, we can multiply 3 by 4, which gives the number 12 and are also factors of 12. These paired factors can be either positive or negative. The list of positive and negative pairs for factors of 12 is given below:

Positive Pair Factors of 12:

The positive pair factors of 12 are (1, 12), (2, 6), and (3, 4).

Positive Pair Factors of 12

Negative Pair Factors of 12:

The negative pair factors of 12 are (-1, -12), (-2, -6), and (-3, -4).

Negative Pair Factors of 12

How To Find Factors of 12 by Division Method?

Now, let’s learn how we can find the factors of 12 through the division method. Firstly, we take integers and then divide them by 12. If the remainder is 0, then it means that they are the factor of 12. If the remainder is 1 or more than that, it means that those numbers are not factors of 12. Here is a step-by-step procedure that will help you to understand how to find factors of 12 using the division method.

  • 12/1 = 12 (Remainder = 0)
  • 12/2 = 6 (Remainder = 0)
  • 12/3 = 4 (Remainder = 0)
  • 12/4 = 3 (Remainder = 0)
  • 12/5 = 2 (Remainder = 2)
  • 12/6 = 2 (Remainder = 0)
  • 12/12 = 1 (Remainder = 0)

The factors of 12 are the numbers, which doesn’t leave any remainder after the division. From the above division, it is clear that the numbers 1, 2, 3, 4, 6, and 12 don’t leave any remainder after division. Hence, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Prime Factorization of 12

In prime factorization, we will write the number 12 as a product of its prime factors. When it comes to the prime factorization of 12, we have to first take a pair factor (1, 12) to divide 12 with. Then we see that 1 is not a composite nor a prime, so we will leave the number. We will now take 12 from the pair. As we know that 12 is a composite digit, we need to divide it with the least prime number that doesn’t leave any remainder.

The steps to find prime factors of 12 are given below:

  • Step 1: Divide the number 12 with the least prime number 2 it is divisible by. (12 ÷ 2 = 6, remainder = 0).
  • Step 2: Divide the number 6 with the least prime number 2 it is divisible by. (6 ÷ 2 = 3, remainder = 0).

As 12 can be noted as a product of 2, 2, and 3, it leads us to the conclusion that 2 and 3 are the prime factors. That explains 12 = 2 x 2 x 3 or 22 X 3.

Prime Factorization of 12

Write the Factor Tree of 12

You can also use a factor tree to find factors of 12. In the factor tree, we separate the numbers and write them as branches. And we will be taking 2 pairs of number 12 can be divided by. Then, we will do this until we reach 1. The final factors are circled and they can be noted as prime factors. Let’s follow these steps to learn and make a factor tree of 12:

  • Step 1: Firstly, we write 12 at the top. Then, divide 12 with the least prime number, which is 2. So the first branch of the factor tree has 2 and 6.
  • Step 2: Now, let’s see if they are prime numbers or not. As 2 is a prime number, just circle it and move on to 6, which is a composite number.
  • Step 3: As we can still divide 6 since it’s a composite number, we further divide with the smallest prime numbers, 2 and 3.
  • Step 4: Now we have 2 and 3 as a new branch. As both are prime numbers, we will circle them, and that’s it for the factor tree.

Lastly, here we can see our prime factors are 22 X 3 or 2 x 2 x 3 = 12.

You can see an example of a factor tree in this image below!

Factor tree of 12

Solved Examples on Factors of 12

Here are some solved examples with questions that are often asked and their answers for kids:

Question: What is the Sum of all the Factors of 12?
Answer:
Factors of 12 are 1, 2, 3, 4, 6, and 12.
If added, the sum will be 28.
Explanation: 1 + 2 + 3 + 4 + 6 + 12 = 28.

Question: What are the factors of 12?
Answer:
1, 2, 3, 4, 6, and 12 are the factors of 12.
12÷1 = 12 (Remainder = 0)
12÷2 = 6 (Remainder = 0)
12÷3 = 4 (Remainder = 0)
12÷4 = 3 (Remainder = 0)
12÷6 = 2 (Remainder = 0)
12÷12 = 1 (Remainder = 0)

Question: What are the common factors of 12 and 8?
Answer:
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 8 are 1, 2, 4, and 8.
Hence the common factors of 12 and 8 are 1, 2, and 4.
If we see the GFC of 12 and 8, it’s 4.

Question: What are the factors of 12 and 28?
Answer: The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 28 are 1, 2, 4, 7, 14, and 28.
Hence the common factors of 12 and 28 are 1, 2, and 4.
If we see the GFC of 12 and 28, it’s 4.

Question: What are the common factors of 12 and 6?
Answer:
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 6 are 1, 2, 3, and 6.
Hence the common factors of 12 and 6 are 6.
If we see the GFC of 12 and 6, it’s 6.

Question: What are the factors and prime factors of 12?
Answer:
The factors and prime factors of 12 are given below:
1, 2, 3, 4, 6, and 12 are the factors of 12.
Whereas 22 × 3 are prime factors of 12.

FAQs on Factors of 12

The frequently asked question regarding factors of 12 are given below:

What are the common factors of 12 and 18?
The factors of 12 are 1, 2, 3, 4, 6, and 12. As for 18, the factors are 1, 2, 3, 6, 9, and 18.
Hence, the common factors of 12 and 18 are 1, 2, 3, and 6.
If we see the GFC of 12 and 18, it’s 6.

What is the number of prime factors of 12?
2 and 3 are the numbers of prime factors of 12.

What is the product of prime factors of 12?
2 x 2 x 3 or 22 x 3 is the product of prime factors of 12.

What are the common factors between 12 and 20?
The factors of 12 are 1, 2, 3, 4, 6, and 12. As for 20, the factors are 1, 2, 4, 5, 10, and 20.
Hence, the common factors of 12 and 20 are 1, 2, and 4.
If we see the GFC of 12 and 20, it’s 4.

What are the factors of -12?
-1, -2, -3, -4, -6, and -12 are the factors of -12.

What are the factors and prime factors of 12?
1, 2, 3, 4, 6, and 12 are the factors of 12.
22 × 3 are prime factors of 12.

We have explained the factors and tree factors of 12. If you have any questions about factors of 12, feel free to comment below, and we will be sure to answer right away. We hope this article helped you!

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Prerit Jain

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