Factors Of 44 | With Easy Division and Prime Factorization

Factors Of 44

Mathematics defines factors of 44 as those numbers that, when multiplied in pairs, give the original number 44. These factors can be both positive and negative. 

Taking 44 as an example, the pair factors can either be (1, 44) or (-1, -44). The result of multiplying the pair of negative numbers, such as -1 and -44, is 44. 44 consists of numbers, neither decimals nor fractions. 

We will examine what are the factors of 44, their prime factors, the pair factors of 44, and how prime factorization can help us find the factors of 44.

What are the Factors of 44?

A factor of a number is the number that divides the number completely without leaving any remainder. In any multiplication, the factors of 44 are the numbers multiplied in pairs and resulting in 44. 

It has six factors and is an even composite number. Due to the presence of factors other than one and the number itself, it is said to be an even composite number.

Factors of 44: 1, 2, 4, 11, 22, 44

Prime Factorization of 44: 22 × 11

What are the Factors of -44?

Factors of -44: -1, -2, -4, -11, -22, -44.

Taking two numbers and multiplying them together to get the number -44 gives:

-1 x  44 =  -44     &   1 x -48 =   -44

-2 x  22 =   -44     &  2 x  -22 =   -44

-4 x  11 =  -44    &  4 x  -11 =   -44

How to Find the Prime Factors of 44?

Here are two steps that help to determine the prime factors of 44. Specifically, they are:

Write down the number 44, which has to be factored.

Identify the two numbers that will produce 44.

Suppose two numbers, say 2 and 22, are the factors.

In this case, 2 is a prime number, and it cannot be split further.

The number 22 can also be factored in as the product of 2 and 11 since it is a composite number. However, both these numbers are prime numbers.

As a result, 44 is written as 2, 2, and 11.

In other words, 44 is equal to 2 × 2 × 11 = 4 × 11 = 44.

Pair Factors of 44

When you multiply two numbers to get 44, you have multiplied two numbers. There are positive and negative pair factors for 44, as discussed above. 

Positive Pair Factors:

Positive pair factors for the number 44 are as follows:

Negative Pair Factors:

Likewise, the negative pair factors are:

Notables:

• A prime number or composite number can be used as a factor of a number, which will divide the number without leaving a remainder.
• There can be negative factors in a number.
• A number’s factor is neither a decimal nor a fraction.

Prime Factorization of 44

The prime factorization method involves writing a number as the product of its prime factors. The following steps will help you find the prime factors of 44.

Write down the factor pairs that, when multiplied, give the original number.

Identify whether the factors are composite or prime.

Multiply the numbers directly if both factors are prime numbers.

Divide the composite number into its prime factors if one of its factors is composite and the other is prime.

Composite factors can be further divided into prime factors if both are composite.

Using the prime factorization method, let’s find the prime factors of 44.

The first step is to take any pair factor of 44. Say (4, 11)

Knowing that 4 and 11 are pair factors, 11 is a prime number and 4 is a composite number

In this case, we have to factor the composite number “4” as the product of 2 and 2

2 × 2

Therefore, 44 can be written as 2 × 2 × 11

As a result, 44 has a prime factorization of 2 × 2 × 11 or 2² × 11.

Examples

Example 1:

Calculate the common factor of 44 and 48.

Solution:

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

Factors of 48 that are prime numbers =   1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Thus, 44 and 48 have two things in common: 1, 2, and 4.

Example 2:

Calculate the common factors between 26 and 53.

Solution:

Factors of 26 are 1, 2, 13, and 26.

Factors of 53 that are prime number = 1 and 53.

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

In this case, 26, 24 and 53 have the same common factors of 1.

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