An Introduction
A factor of an integer is another integer that can divide the integer without leaving any remainder. When multiplied in pairs, the numbers that provide the original number 44 are known as 44's factors. The pair factors of 44 might have both positive and negative values. The pair factors of 44, for instance, might be \[\left( 1,\text{ }44 \right)\] or \[\left( -1,\text{ }-44 \right)\]. When two negative numbers are multiplied, such as when \[-1\] and \[-44\] are multiplied, the answer is 44. The factors of 44, their prime factors, their pair factors, and how to determine the factors of 44 using the prime factorization method are all covered in this article.
What are the Factors of 44?
The factors of 44 are the numbers that divide 44 exactly with no remainder. Since the number 44 is an even composite, it has many factors other than 1 and 44. There are 6 factors in 44. As a result, the factors of 44 are 1, 2, 4, 11, 22, and 44.
How to Determine the Factors of 44?
The two steps help us to find 44's factors. As follows:
Step 1: Write the number 44, which has to be factored in.
Step 2: Find the two numbers whose product is 44.
Consider the integers 2 and 22 to be the two factors. In this case, 2 is a prime number that cannot be divided further.
Take another number, 22, which is a composite number that may be factored further as the product of 2 and 11. Both integers are now prime numbers.
So, 44 is expressed as the product of \[2\times 2\times 11\]\[=4\times 11\]
Thus, the factors of 44 are 1, 2, 11, 22, and 44.
Factors of 44 by Prime Factorization
44 is a composite number that should have prime factors. Prime factorization of 44 refers to determining the prime factors of 44. Divide 44 by the smallest prime number possible to get the prime factor of 44. Then, take the result and divide it by the lowest prime number. Repeat this step until you have 1.
Step 1: Divide 44 by 2
\[44\div 2=22\]
Step 2: Again, divide 22 by 2
\[22\div 2=11\]
Step 3: 11 is a prime number. So, divide 11 by 11
\[11\div 11=1\]
Thus, we get 1 at the end of this division method, and we can’t go on with the division approach. Hence, the prime factor of 44 is \[2\times 2\times 11\] or \[{{2}^{2}}\times 11\] where 2 and 11 are prime numbers.
Factor Tree of 44
We know that the prime factor of 44 is \[2\times 2\times 11\] or \[{{2}^{2}}\times 11\] where 2 and 11 are prime numbers. See it prime factor tree below.
Factor Tree of 44
Factors of 44 in Pairs
The pair factors of 44 might have both positive and negative values. The pair factors of 44, for instance, might be \[\left( 1,\text{ }44 \right)\] or \[\left( -1,\text{ }-44 \right)\]. When two negative numbers are multiplied, such as when \[-1\] and \[-44\] are multiplied, the answer is 44. Pair factors of 44 are as follows:
Positive Factors of 44
Thus, the positive pair factors are \[\left( 1,\text{ }44 \right),\text{ }\left( 2,\text{ }22 \right)\] and \[\left( 4,\text{ }11 \right)\].
Negative Factors of 44
Thus, the negative pair factors are \[\left( -1,\text{ }-44 \right),\text{ }\left( -2,\text{ }-22 \right)\] and \[\left( -4,\text{ }-11 \right)\].
Interesting Facts
Every number has at least two factors which are one and the number itself
A composite number can be divided further into its factors.
Important Questions
1. Find the common factors of 150 and 160.
Ans: An integer that has been divided by the original number into equal parts without a remainder is called a factor. A number that divides each provided number perfectly is known as a common factor of two or more numbers.
So, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150 and the factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
Thus, the common factors of 52 and 62 are 1, 2, 5, and 10.
2. Draw a factor tree of 55.
Ans: We know that the prime factor of 55 is \[5\times 11\], where 5 and 11 are prime numbers. See it prime factor tree below.
Factor Tree of 55
3. What is the HCF of 66 and 77?
Ans: The highest common factor, or HCF, is the biggest number that divides each of two or more numbers. The factors of 66 and 77 are 1, 2, 3, 11, 22, 33, 66 and 1, 7, 11, 77 respectively.
HCF is to find which factors are common to both 66 and 77.
11 is common factor for both 66 and 77
Therefore, the HCF of 66 and 77 is 11.
Practice Questions
1. What is the HCF of 88 and 99?
22
33
11
1
2. What is the sum the of factors of 33?
28
38
49
48
Answers:
Option C
Option D
Conclusion
In this article we learned about factors of 44 and the prime factorization of 44. Hence, the number 44 is even composite, it has many factors other than 1 and 44. As a result, all the factors of 44 are 1, 2, 4, 11, 22, 44 and the prime factor of 44 is \[{{2}^{2}}\times 11\], where 2 and 11 are prime numbers.
FAQs on Finding the Factors of 44
1. Can 2 be a factor of all numbers?
No. Since 2 can only divide even numbers and not odd ones, such as 11, 17, 15, or 33, it cannot be the factor of all numbers.
2. Define prime numbers
There are only 2 factors for prime numbers, which are 1 and itself. The only ways to divide these integers without leaving a remainder are by 1 and the number itself. Prime numbers are: 2, 3, 5, 7, 11, 13, …
3. Define composite numbers
There are more than two factors in composite numbers. It can be divided by at least one positive integer, in addition to being divided by 1 and the number itself.
Example: Factors of 38 are 1, 2, 19 and 38.
