Factors

Factors of 33 | Prime Factorization of 33 | Factor Tree of 33

Written by Prerit Jain

Updated on: 18 Aug 2023

Factors of 33 | Prime Factorization of 33 | Factor Tree of 33

The factors of 33 are 1, 3, 11, and 33. A list of numbers that divides a given number evenly is known as its factors. For 33, the numbers 1, 3, 11, and 33 will divide the number 33 evenly. Hence, there are a total of 4 factors for the number 33.

The factors of a number can be both positive and negative and are also written in the pair format. This means that multiplying the set of two factors in pairs gives the original product (33). In this article, let us discuss how to find factors of 33, its prime factorization, and factor trees with solved examples. Continue reading to learn more.

What Are the Factors of 33?

The factors of 33 are the numbers that divide the number (33) evenly without leaving any remainder. The factors of a number can be both positive and negative. Hence, the number 33 has both positive and negative factors.

What Are the Factors of 33 in Pairs?

A pair factor of 33 is a combination of two numbers, which when multiplied together gives the product of the original number (33). These pair factors are also written in positive and negative pairs as shown in the table below:

Positive Pair Factors of 33

The positive pair factors of 33 are (1, 33), (3, 11), (11, 3), and (33, 1).

Negative Pair Factors of 33

The negative pair factors of 33 are (-1, -33), (-3, -11), (-11, -3) and (-33, -1).

How To Find Factors of 33 Using the Division Method?

To determine the factors of 33, we are using the division method. This approach requires you to multiply a sequence of natural numbers by 33. The numbers that divide 33 completely without leaving any remainder are known as 33 factors. The following are the detailed steps for finding factors of 33 using the division method:
33 ÷ 1 = 33
33 ÷ 3 = 11
33 ÷ 11 = 3
33 ÷ 33 = 1

Therefore, we can see that 1, 3, 11, and 33 are the numbers that do not leave any remainder when divided by 33. Hence, the factors of 33 are 1, 3, 11, and 33.

What Is the Prime Factorization of 33?

Check if the given number is a prime number. If the given number is a prime number, then it has only two factors: 1 and 33. If the given number is a composite number, then it has more than two factors.
Since 33 is the composite number, we have more than two factors. Hence, we can use the prime factorization method to find the factors of 33.

The steps to find prime factors of 33 using the prime factorization method are given below:

Step 1: Divide the number 33 by the smallest prime number that is divisible by 33. Hence, the smallest prime number that is divisible by 33 is 3.
So, 33 ÷ 3 = 11

Step 2: Now, divide the number 11 (quotient) next. But since 11 is a prime number by itself, it can be divided only by 1 and 11.
So, 11 ÷ 11 = 1
The quotient is 1. Since 1 cannot be divided further, the prime factors of 33 are 3 X 11. We can also write it down as 3 and 11, as both of them are prime numbers.

Image representation of the prime factorization of 33:

What is the Factor Tree of 33?

Students can also use the factor tree to find the prime factors of 33. In this method, we will place the number 33 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (33). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 33

Step 1: Let’s place the number 33 at the top of the factor tree and write down 33 in pairs, that is, 3 and 11.

Step 2: Since 3 is a prime number, we can no longer separate it. 11 is also a prime number. So we cannot separate 11 either. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 3 X 11= 33, which are the prime factors of 33.

There are many ways in which we can write the factor tree of 33. Below is an image representation of the factor tree of 33, choosing 3 and 11 as pair factors of 33.

Solved Examples on Factors of 33

Here are some solved examples of 33 factors:

What is the sum of all the factors of 33?
1, 3, 11, and 33 are the factors of 33.
1 + 3 + 11 + 33 = 48
Hence, 48 is the sum of all 33 factors.

What are the factors and prime factors of 33?
The factors of 33 are 1, 3, 11, and 33.
The prime factors of 33 are 3 and 11.

What’s the highest common factor between 44 and 33?
The factors of 44 are 1, 2, 4, 11, 22, and 44.
Factors of 33 are 1, 3, 11, and 33.
Hence, from the above, the common factors of 44 and 33 are 1 and 11.
The highest common factor between 44 and 33 is 11.

What’s the highest common factor between 15 and 33?
The factors of 15 are 1, 3, 5, and 15.
Factors of 33 are 1, 3, 11, and 33.
Hence, from the above, the common factors of 15 and 33 are 1 and 3.
The highest common factor between 15 and 33 is 3.

Is 11 a factor of 33?
Yes, 11 is a factor of 33.
As 33 ÷ 3 = 11.

What are the factors of -33?
The factors of -33 are -1, -3, -11 and -33.

What are the common factors of 35 and 33?
To find the common factors of 35 and 33, we need to find the factors of both 35 and 33.
Factors of 48: 1, 5, 7 and 35
Factors of 33: 1, 3, 11 and 33
Hence the common factor of 35 and 33 is 1.

What are all the factors of 33?
The factors of 33 are 1, 3, 11, and 33.

What are the factors of 33 that are composite?
Any number which has more than 2 factors is known as a composite number. The list of number which has more than 2 factors in factors of 33 is 33.

What factors of 33 are multiples of 3?
The factors of 33 that are multiples of 3 are 3 and 33.
3 x 1 = 3
3 x 11 = 33

How many factors of 33 are odd?
All factors of 33 are odd. They are 1, 3, 11, and 33.

What are the common factors of 77 and 33?
To list out the common factors of 77 and 33, we need to find the factors of both 77 and 33.
Factors of 77: 1, 7, 11 and 77
Factors of 33: 1, 3, 11 and 33
Hence, the common factors between 77 and 33 are 1 and 11.

How many pair factors are there in 33?
A total of 2 pairs are there in factors of 33.

What is the largest factor of 33?
The largest factor of 33 is 33.
The second largest factor of 33 is 11.

FAQs on Factors of 33

List all the factors of 33
1, 3, 11, and 33 are the 33 factors.

What are the composite factors of 33?
33 is the only composite factor of 33. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 33 in pairs?
(1, 33) and (11, 3) are the 33 factors of pairs.

What are the positive factors for 33?
1, 3, 11, and 33 are the positive factors for 33.

What is the co-prime of 33?
Co-prime numbers are those numbers that have only one common factor, namely 1.
33 and 7 have only one common factor which is 1. This implies that 33 and 7 are co-prime.

Now that you have all the necessary information regarding the factors of 33, We hope this blog has been useful for you and easy to understand as well.

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Prerit Jain

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