In Mathematics, the factors of 44 are the numbers which when multiplied in pairs will result in an original number 44. The pair factors of 44 can be positive as well as negative. For example, the pair factors of 44 can be (1, 44) or (-1, -44). If we multiply the pair of negative numbers, such as multiplying -1 and -44, it will result in 44. The factors of 44 are the numbers, which are neither decimals nor fractions. Here, we will learn what are the factors of 44, its prime factors, pair factors of 44, and how to find the factors of 44 using the prime factorization method.
Table of Contents:
- What are the Factors of 44?
- How to Find the Prime Factors of 44?
- Pair Factors of 44
- Prime Factorization of 44
- Solved Examples
- FAQs
What are the Factors of 44?
We know that the factors of a number are the numbers that divide the number completely without leaving any remainder. The factors of 44 are the numbers that are multiplied in pairs and give the product as 44. The number 44 is the even composite number and it has 6 factors. It is said to be an even composite number, as it has factors other than one and the number itself.
Factors of 44: 1, 2, 4, 11, 22, 44 Prime Factorization of 44: 2^{2} × 11 |
How to Find the Prime Factors of 44?
The following two steps help to find the prime factors of 44. They are:
Step 1: Write down the number 44, which has to be factorized.
Step 2: Determine the two numbers, whose product will be 44.
For example, let us take two numbers 2 and 22 to be the two factors.
Here, 2 is a prime number, and it cannot be split further.
Now, take another number 22, which is a composite number, and it can further be factored as the product of 2 and 11. Now, both the numbers are prime numbers.
Thus, 44 is written as the product of 2, 2 and 11
It means that 44 can be written as 2 × 2 × 11 = 4 × 11 = 44
Also, read: |
Pair Factors of 44
The pair factors of 44 are the multiplication of a pair of numbers which results in the original number 44. As discussed above, the pair factors of 44 can be written in the positive pairs as well as in the negative pairs. The number 44 has the following positive pair factors:
Positive Factors of 44 |
Positive Pair Factors of 44 |
1 × 44 |
(1, 44) |
2 × 22 |
(2, 22) |
4 × 11 |
(4, 11) |
Similarly, the negative pair factors are:
Negative Factors of 44 |
Negative Pair Factors of 44 |
-1 × -44 |
(-1,-44) |
-2 × -22 |
(-2, -22) |
-4 × -11 |
(-4, -11) |
Points to Remember:
- Factors of a number can be a prime number or composite number, that can divide the number completely without leaving a remainder.
- Factors of a number can be negative.
- Factors of a number are neither decimals nor fractions.
Prime Factorization of 44
The method of writing the number as the product of its prime factors is called the prime factorization method. Follow the procedure given below to find the prime factors of a number 44.
Step 1: Write down the factor pairs, which on multiplication gives the original number.
Step 2: Check whether the factors are prime or composite.
- If both the factors are prime numbers, multiply the numbers directly.
- If one factor is composite, and the other factor is prime, then split the composite numbers into its prime factors.
- If both the factors are composite they can be further split into their prime factors.
Now, let us learn how to find the prime factors of 44 using the prime factorization method.
Step 1: Take any one of the pair factors of 44. Say (4, 11)
Step 2: From the pair factor (4, 11), 11 is a prime number and 4 is a composite number
So, here we have to factor the composite number “4” as the product of 2 and 2
(i.e) 2 × 2
Thus, 44 can be written as 2 × 2 × 11
Therefore, the prime factorization of 44 is 2 × 2 × 11 or 2^{2} × 11.
Examples
Example 1:
Find the common factors of 44 and 38.
Solution:
Factors of 44 = 1, 2, 4, 11, 22, 44.
Factors of 38 = 1, 2, 19, 38.
Hence, the common factors of 44 and 38 are 1 and 2.
Example 2:
Determine the common factors of 44 and 56.
Solution:
The factors of 44 are 1, 2, 4, 11, 22, 44.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
Therefore, the common factors of 44 and 56 are 1, 2 and 4.
Frequently Asked Questions on Factors of 44
What are the factors of 44?
The factors of 44 are 1, 2, 4, 11, 22 and 44.
Write down the prime factorization of 44.
The prime factorization of 44 is 2 × 2 × 11 or 2^{2} × 11.
Is 44 a prime number?
No, 44 is not a prime number. The number 44 is an even composite number. Apart from one and the number itself, 44 has many factors.
Mention the pair factors of 44.
The pair factors of 44 are (1, 44), (2, 22) and (4, 11).
Can a number have negative pair factors?
Yes, a number can have negative pair factors, For example, the negative pair of 44 is (-1, -44), which on multiplication gives the original number 44.