Factors Of 33 | With Easy Division and Prime Factorization

Factors Of 33

Factors of 33 are the numbers that multiply to produce 33. If we multiply 3 and 6, we get 18, i.e. 3  × 6 = 18, so 3 and 6 are factors of 18. We can find the factors of 33 in the same way.

In this article, you will learn how to find the factors of a number and prime factors of 33.

What are the Factors of 33?

Because 33 is a composite number, it has more than two factors, meaning there are factors besides 1 and 33.

Factors of 33:

1, 3, 11, and 33

Furthermore, we know the exact factors of 33 are divisors of this number. We can find its factors in two ways for any given number, either through division or by the factor pair method.

What Are The Factors Of -33

Factors of -33:  1, 3, 11, and 33

When we multiply two numbers to get the product -33, it comes the following:

-1 x  33 =  -33

-3 x 11 = -33

Similarly

1  x  -33 = -33

3  x -11 = -33

Therefore,  we have the possible pairs of factors of -33 as (-1 x  33), (-3 x 11) or (1 x -33) and (3 x -11).

How to Find the Factors of 33?

You can learn how to find the factors of 33 by following the steps below.

Write the number 33 in your notebook first.

Multiply the two numbers, that will give 33, such as 3 x 11 = 33.

Obviously, 3 only has two factors, 1 and itself, since 3 is a prime number. So, You can’t further factorize it.

3 = 1 × 3

In addition, 11 is a prime number that cannot be factored further.

11 = 1 × 11

As a result of factorizing 33, we get 1 × 3 × 11.

Based on the above expression, the following unique numbers are obtained: 1, 3, 11, and 33

The factor of 33 in Pairs

Any number can have both positive and negative factors. Multiply the two numbers in a pair to have the original 33 as the pair factor. Here are some such numbers:

Consequently, the positive pair factors for 33 are (1, 33), (3, 11), (11, 3) and (33, 1).

Among the negative pair factors of 33, there are (-1, -33), (-3, -11), (-11, -3) and (-33, -1).

Notables:

Below are a few key facts about 33:

• There are four factors in 33.
• The sum of all factors of 33 equals 48.
• Each factor of 33 is equal to the square of 33.
• Since 33 is an odd number, all its factors are also odd. But not all odd numbers have odd factors and the same for even numbers, 36 is an even number but it has even and odd factors.

Solved Examples 

Example 1:

What are the common factors between 36, 24, and 75?

Solution:

1, 2, 3, 4, 6, 8, 12, and 24 are the factors of 24.
1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36.

Factors of 75 are 1, 3, 5, 15, 25, and 75.
24, 33, and 75 have 1 and 3 in common.

How to calculate Prime Factors of 33?

The prime factors of 33 can be written as follows by the prime factorization method.

Divide 33 by the smallest prime number, i.e., 2.

33 ÷ 2 = 16.5

Since the factors cannot be fractions, 2 is not the prime factor for 33.

Continue with the following prime numbers, i.e., 3, 5, 7, etc.

33 ÷ 3 = 11, and 3 and 11 are prime numbers, so we cannot divide them.

Consequently, the prime factorization of 33 is 3 × 11.

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