Factors of 44

Factors of 44 are the list of integers that can be evenly divided into 44. There are 6 factors of 44 of which 44 itself is the biggest factor and its positive factors are 1, 2, 4, 11, 22, and 44. The Prime Factors and Pair Factors of 44 are 1, 2, 4, 11, 22, 44 and (1, 44), (2, 22) and (4, 11) respectively.

• Factors of 44: 1, 2, 4, 11, 22 and 44
• Negative Factors of 44: -1, -2, -4, -11, -22 and -44
• Prime Factors of 44: 2, 11
• Prime Factorization of 44: 2 × 2 × 11 = 2² × 11
• Sum of Factors of 44: 84

What are the Factors of 44?

Let us recall the meaning of the term 'factor'.

• A factor is a number that divides into another number completely without leaving any remainder.
• Factors of 44 are the numbers which when multiplied together result in 44
• 4 and 11 are the factors of 44
• This means that 4 divides 44 into equal parts of 11 each.

4 × 11 = 44

However, it should be noted that 44 does not have 4 and 11 as its only factors. It has other factors as well.
Let us see how to calculate the factors of 44

How to Calculate the Factors of 44?

• Step 1: Write down the number to be factored, that is, 44
• Step 2: Find the two numbers whose product is 44

Let's say we take 4 and 11 to be the two factors.
11 is a prime number, therefore, it cannot further be split.
4 is not a prime number. Hence, it can be factorized as a product of 2 and 2, apart from the product of 1 and the number itself.
4 can be written as 2 × 2 = 4.
Hence, 44 can be written as: 44 =  2 × 2 × 11
Factors of 44 are 1, 2, 4, 11, 22, 44

Explore factors using illustrations and interactive examples.

• Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
• Factors of 441 - The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441
• Factors of 43 - The factors of 43 are 1, 43
• Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 
• Factors of 49 - The factors of 49 are 1, 7, 49
• Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45

Factors of 44 by Prime Factorization

Prime factorization is the process of writing a number as a product of its prime factors.
Let us learn how to find the factors of a number using prime factorization.

• Step 1: Write the pair of factors, which on multiplication give the required number.
• Step 2: Check whether the factors are prime or not.
• If both the numbers are prime, they can be multiplied as it is. 
• If one of them is prime and the other one is composite, then the composite number is further split into its factors.
• If both the numbers are composite, they can be further split into their factors.

Let us find the factors of 44 by prime factorization using these steps.

• Step 1: 44 can be factored as a product of 4 and 11
• Step 2: 4 is not a prime number and can further be factored as a product of 2 by 2 or as a square of 2
• Step 3: Therefore, 44 can be written as:

44 = 4 × 11 = 2× 2× 11

It can also be written as 44 = 2² × 11

Observe this factor tree.

Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.

Important Notes:

• Factors of any number are all the possible numbers that can divide the number without leaving any remainder.
  They may be prime numbers or composite numbers
• Factors can never be fractions or decimals
• Factors can be negative

Factors of 44 in Pairs

Factors are often written as pairs of numbers, which when multiplied together give the original number. Here, the required number is 44. 44 can have the following pair factors:

• The factors given above are the positive pair factors of 44
• It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.
• Let's have a look at the negative pair factors of 44:

Tips and Tricks:

• 1 is the smallest factor of every number.
• Every number has a minimum of 2 factors, that is, 1 and the number itself.
• All even numbers always have 2 as one of their factors. For example factors of 44 are 1, 2, 4, 11, 22, 44.

Challenging Questions:

• What are the factors of the following numbers using the prime factorization method?

1. 444
2. 4444
3. 444444