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Methods to Find the Factors of 33

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Last updated date: 29th Feb 2024
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An Introduction to the Factors of 33

The numbers that when multiplied together result in the number 33 are called factors of 33. For instance, when we multiply 2 and 7, we get 14, which means that \[7\times 7\text{ }=\text{ }14\] and that 2 and 7 are factors of 14. The factors of the number 33 may be discovered in the same way. You will learn the factors of 33, how to discover the factors of a number 33, and the prime factors of 33 in this post, along with clear instructions.


What are the Factors of 33?

An integer that has been divided by the original number into equal parts without a remainder is called a factor. So, the factors of 33 are the numbers that divide 33 exactly with no remainder. Hence, the factors of 33 are 1, 3, 11 and 33.


How Can We Find the Factors for 33?

To calculate the factor of 33, just divide 33 by all the integers from 1 to 33. Also, find the integer that divides 33 without leaving a remainder. Let's do it and figure out all the 33 factors.

\[33\div 1=33\]

1 is a factor of 33.

\[33\div 3=11\]

3 is a factor of 33.

\[33\div 11=3\]

11 is a factor of 33.

\[33\div 33=1\]

33 is a factor of 33.

Hence, the factors of 33 are 1, 3, 11, and 33.


Prime Factorization of 33

The set of prime numbers whose product is 33 is known as the prime factorisation of the number 33. Divide 33 by the smallest prime number possible to get the prime factor of 33. Then, take the result and divide it by the lowest prime number. Repeat this step until we have 1.

The first step is to divide 33 by the lowest prime integer, which is 2.

\[33\div 2=16.5\]

It can’t be a factor, so go to the next prime number, i.e., 3

\[33\div 3=11\]

Since 3 and 11 are prime numbers, we cannot use the division method.

Hence, the prime factor of 33 is \[3\times 11\], where 3 and 11 are prime numbers.


Prime Factor Tree of 33

Factor tree represents the factors of a number, especially its prime factorisation. Each tree branch is divided into factors. The end of the branch in the factor tree must be a prime number because the only two factors are itself and one, so the branch stops.

Factor Tree of 33 is given below:


Factor Tree of 33


Factor Tree of 33


Factors of 33 in Pairs

Pair factors may be positive or negative, but they cannot be a fraction or a decimal. To get the pair factor of 33, multiply the two numbers in a pair to obtain the original number, which is 33, as follows:

Positive Factors of 33

Factor Pair of 33

\[1\times 33\]

\[\left( 1,\text{ }33 \right)\]

\[3\times 11\]

\[(3,\text{ }11)\]

\[11\times 3\]

\[\left( 11,\text{ }3 \right)\]

\[33\times 1\]

\[\left( 33,\text{ }1 \right)\]


So, the positive pair factors of 33 are \[\left( 1,\text{ }33 \right)\], \[(3,\text{ }11)\], \[\left( 11,\text{ }3 \right)\] and \[\left( 33,\text{ }1 \right)\].


Negative Factors of 33

Factor Pair of 33

\[-1\times -33\]

\[\left( -1,\text{ }-33 \right)\]

\[-3\times -11\]

\[\left( -3,\text{ }-11 \right)\]

\[-11\times -3\]

\[\left( -11,\text{ }-3 \right)\]

\[-33\times -1\]

\[\left( -33,\text{ }-1 \right)\]


So, the negative pair factors are \[\left( -1,\text{ }-33 \right)\], \[\left( -3,\text{ }-11 \right)\], \[\left( -11,\text{ }-3 \right)\] and \[\left( -33,\text{ }-1 \right)\].


Interesting Facts

  • 33 has a total of 4 factors. The total of all 33 factors equals 48.

  • Since 33 is an odd number, all of its factors are likewise odd numbers.


Solved Important Questions

1. Find common factors of 33 and 39.

Solution: A factor is an integer that is divided by the original number into equal parts without the remainder. A number that divides each of the provided numbers perfectly is a common factor of two or more numbers.

Hence, factors of 33 and 39 are 1, 3, 11, and 33 and 1, 3, 13, and 39, respectively.

Therefore, the common factors of 33 and 39 are 1 and 3.


2. Find the factors of 44 and 55.

Solution: The factors of 44 are the numbers that divide 44 exactly with no remainder. So,

\[44\div 1=44\]

\[44\div 2=22\]

\[44\div 4=11\]

\[44\div 11=4\]

\[44\div 22=2\]

\[44\div 44=1\]

Therefore, the factors of 44 are 1, 2, 4, 11, 22, and 44.

Similarly, the factors of 55 are 1, 5, 11, and 55.


3. Find the multiples of 33 and the sum of its first 3 multiples.

Ans: A number and a counting number are known as a multiple of the original number. So, the multiples of 33 are 33, 66, 99, 132, 165, 198, 231, …

Sum of its first 3 multiples \[=33+66+99=198\].


Conclusion

The numbers that divide 33 exactly with no remainder are known as the factors of 33. The factors of 33 are 1, 3, 11, and 33. The prime factorization of 33 is 3x11, where 3 and 11 are prime numbers. The positive pair factors of 33 are \[\left( 1,\text{ }33 \right)\], \[(3,\text{ }11)\], \[\left( 11,\text{ }3 \right)\] and \[\left( 33,\text{ }1 \right)\] and the negative pair factors are \[\left( -1,\text{ }-33 \right)\], \[\left( -3,\text{ }-11 \right)\], \[\left( -11,\text{ }-3 \right)\] and \[\left( -33,\text{ }-1 \right)\]


Practice Question

1. How many factors does 150 have?

  1. 10

  2. 11

  3. 12

  4. 13

Ans: Option D


2. Which one is correct?

  1. The prime factorisation of 52 is \[4\times 5\times 13\]

  2. The prime factorisation of 150 is \[2\times 3\times 5\times 5\]

  3. The prime factorisation of 37 is \[3\times 13\]

  4. The prime factorisation of 9 is \[2\times 3\]

Ans: Option B

FAQs on Methods to Find the Factors of 33

1. Find all the factors of 33.

The numbers that divide 33 exactly with no remainder are known as the factors of 33. So, all the factors of 33 are 1, 3, 11, and 33.  The prime factorization of 33 is 3x11, where 3 and 11 are prime numbers. The positive pair factors of 33 are \[\left( 1,\text{ }33 \right)\], \[(3,\text{ }11)\], \[\left( 11,\text{ }3 \right)\] and \[\left( 33,\text{ }1 \right)\] and the negative pair factors are \[\left( -1,\text{ }-33 \right)\], \[\left( -3,\text{ }-11 \right)\], \[\left( -11,\text{ }-3 \right)\] and \[\left( -33,\text{ }-1 \right)\]

2. How to find the prime factors of 7429?

The prime factors of a number are those factors of the given number which divide it exactly and are also prime. The factors of 7429 can be found using the division method or the factor tree method. The factors of 7429 are 1, 17, 19, 23, 323, 391, 437, and 7429. However, the prime factors of 7429 can be computed using the prime factorisation of 7429. The prime factorisation of 7429 is $7429\;=\;17\; \times \;19\; \times \;23$. Hence, the prime factors of 7429 are 17, 19, and 23.