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Factors

Factors of 36 | What Are the Prime Factors of 36?

Written by Prerit Jain

Updated on: 04 Dec 2023

Contents

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Factors of 36 | What Are the Prime Factors of 36?

Factors of 36 | What Are the Prime Factors of 36?

Factors are the numbers that leave no remainder after division. The factors of 36 can be both positive and negative. There are a total of 9 factors for the number 36, where 1 is the smallest factor and 36 is the largest factors of 36. The prime factors of 36 are 2 and 3. In this article, let us understand how to find factors of 36 using various methods with solved examples. Scroll down to find out more.

What Are the Factors of 36?

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Since 36 is a composite number, there are multiple factors for the number 36. Hence, the total number of factors for 36 is 9.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36
Negative Factors of 36-1, -2, -3, -4, -6, -9, -12, -18, and -36
Prime Factorization of 36: 2 × 2 × 3 × 3 or 22 X 32
Prime Factors of 36: 2, 3
Sum of Factors of 3691
Sum of Prime Factors of 36: 5

Factors of 36 in Pairs

Like we said above, there are 9 factors for the number 36. The factors of 36 have both positive and negative pairs. Let us see the positive pair and the negative pair of factors of 36:

Factors of 36 in Positive Pairs

The factors of 36 in positive pairs are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).

Positive Pair Factors of 36

Factors of 36 in Negative Pairs

The factors of 36 in negative pairs are (-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).

Negative Pair Factors of 36

Prime Factorisation of 36

In Maths, to find the prime factorisation of the number 36, we must write the numbers as the product of prime factors of 36.

To find the prime factors of 36, divide it by 2, which is the smallest prime number. When we can no longer divide it with 2, we must divide it with the next small prime number, which is 3. We will repeat this process until the product reaches 1. This entire process is known as prime factorization.

  • Step 1: Divide 36 by the smallest prime number 2. We are also dividing 30 by 2 because it is the smallest prime number that 30 is divisible by.
    • 36 ÷ 2 = 18
  • Step 2: Now again divide 18 with the smallest prime number which is 2.
    • 18 ÷ 2 = 9
  • Step 3: Since 9 cannot be divided by 2. Hence, we will divide the number 9 by the next smallest prime number which is 3. Because it is the smallest prime number 9 is divisible by.
    • 9 ÷ 3 = 3
  • Step 4: Lastly, 3 cannot be divided by 2. Hence, we are dividing 3 by 3 and we get the product 1.
    • 3 ÷ 3 = 1

Hence the prime factorization of 36 is 2 x 2 x 3 x 3. The prime factors of 36 = 22 × 32.

Prime Factorization of 36
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Factor Tree of 36

Students can also use the factor tree for the prime factorization of 36. In a factor tree, we divide a number until the answer becomes 1, and the factors are written in the form of branches of a tree. Then, the last factors are circled, and they are the prime factors of the number. The detailed steps on how to do this are explained below:

  • Step 1: Firstly, we will separate the 36 into two factors. For this, we can select 2 and 18 as pair factors of 36. As 2 is the smallest number 36 can be divided by, and after dividing 2 by 36, we receive 18.
  • Step 2: Now, let’s see if they are prime numbers or not. 2 is a prime digit, so we can circle it. But since 18 is a composite number, we divide it further with the smallest prime pair numbers it can be divided by.
  • Step 3: We repeat our observation, this time circling 2 because it is a prime digit. But since 9 is not a prime number, we separate it into the smallest prime numbers pair we can.
  • Step 4: After dividing, we can see 3 and 3. So, after noticing that 3 is a prime number, we circle it, and since we are done with the divination, we see the numbers we have circled.
  • Step 5: We are left with 2 and 3. So, that concludes that 2 × 2 × 3 × 3 = 36 are prime factors of 36. 

Remember that there are many ways people make factor trees of 36, so you can also start by separating 9 and 4 from 36 instead of 2 and 18. Then, they can be split further. Lastly, you’ll find that they have the same prime factors as 36 = 2 × 2 × 3 × 3. No matter how you go about separating the numbers for the factor tree.

Factor tree of 36

Solved Examples on Factors of 36

Here are some solved examples of factors of 36 for you:

Question: What are the factors of 36 that add up to 12?
Answer:
You can find the answer by listing all the factors of 36. Then, you have to divide all the different combinations and add up to 12 total. The factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. After adding them, you can find the combinations that make up 12. Here they are:
3 + 9 = 12
6 + 6 = 12
9 + 3 = 12
So, 3, 6, and 9 are the factors of 36 that add up to 12.

What are the common factors of 36
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36
1, 2, 3, 4, 6, 9, 12, 18, and 36 are the common factors of 36

Question: What are the factors of 36 and 48?
Answer:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
If we see the common factor of 36 and 48 is 12.
You can find factors for them through division, multiplication, and prime factorization.

Question: What are the factors of 36 that add up to 13?
Answer:
You can find the answer by listing all the factors of 36. Then, you have to divide all the different combinations and add up to 13 total. The factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. After adding them, you can find the combinations that make up 13. Here they are:
1 + 12 = 13
4 + 9 = 13
9 + 4 = 13
12 + 1 = 13
So, 1, 4, 9, and 12 are the factors of 36 that add up to 13.

Question: What are the factors of 36 that add up to 5?
Answer:
You can find the answer by listing all the factors of 36. Then, you have to divide all the different combinations and add up to 5 total. The factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. After adding them, you can find the combinations that make up 5. Here they are:
1 + 4 = 5
2 + 3 = 5
3 + 2 = 5
4 + 1 = 5
So, 1, 2, 3, and 4 are the factors of 36 that add up to 5.

Question: What are the factors of 36 and 54?
Answer:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
And the factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
If we see the GFC of 36 and 54, there is 18.
You can find factors for them through division, multiplication, and prime factorization.

Question: What are the factors of 36 that are composite numbers?
Answer:
Composite numbers are the ones that are described as whole digits and have three or more whole number factors.
1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36.
Composite Numbers of 36: 4, 6, 9, 12, 18, and 36 are the factors of 36 that are composite numbers.

What are the factors of -36?
-1, -2, -3, -4, -6, -9, -12, -18, and -36 are the factors of -36.

FAQs on Factors of 36

What are the common factors between 36 and 24?
Out of all the factors, there are 6 common factors between 36 and 24.
They are 1, 2, 3, 4, 6, and 12.

What are the prime factors of 36?
22 × 32 are the prime factors of 36.

What is the product of prime factors of 36 is ____?
2² × 3² = 36 is the product of the prime factors of 36.
We can even write it as 2² × 3² = 36.

What are the common factors of 36 and 12?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
As for 12, the factors are 1, 2, 3, 4, 6, and 12.
The common factors of 36 and 12 are 1, 2, 3, 4, 6, and 12.
If we see the GFC of 36 and 48, it’s 12.

What are the factors and prime factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36.
Furthermore, primer factors of 36 are 2 X 2 X 3 X 3 = 22 × 32 = 36.

So, that’s all about factors and prime factors of 36. We hope that this has been useful for you and you can easily find factors of 36 and even use all the methods to find factors too. If you do have any questions or doubts, feel free to leave a comment below and we will surely check it out and present you with an answer.

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Prerit Jain

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