MATH SOLVE

2 months ago

Q:
# What are the Factors of 44?

Accepted Solution

A:

Factors of 44
Methods
What are the Factors of 44?
The following are the different types of factors of 44:
• Factors of 44: 1, 2, 4, 11, 22, 44
• Sum of Factors of 44: 84
• Negative Factors of 44: -1, -2, -4, -11, -22, -44
• Prime Factors of 44: 2, 11
• Prime Factorization of 44: 2^2 × 11^1
There are two ways to find the factors of 44: using factor pairs, and using prime factorization.
The Factor Pairs of 44
Factor pairs of 44 are any two numbers that, when multiplied together, equal 44. The question to ask is “what two numbers multiplied together equal 44?” Every factor can be paired with another factor, and multiplying the two will result in 44.
To find the factor pairs of 44, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 44. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.
Step 2:
Divide 44 by the smallest prime factor, in this case, 2:
44 ÷ 2 = 22
2 and 22 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 22 as the new focus. Find the smallest prime factor that isn’t 1, and divide 22 by that number. In this case, 2 is the new smallest prime factor:
22 ÷ 2 = 11
Remember that this new factor pair is only for the factors of 22, not 44. So, to finish the factor pair for 44, you’d multiply 2 and 2 before pairing with 11:
2 x 2 = 4
Step 4:
Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.
Here are all the factor pairs for 44:
(1, 44), (2, 22), (4, 11)
So, to list all the factors of 44: 1, 2, 4, 11, 22, 44
The negative factors of 44 would be: -1, -2, -4, -11, -22, -44
Prime Factorization of 44
To find the Prime factorization of 44, we break down all the factors of 44 until we are left with only prime factors. We then express n as a product of multiplying the prime factors together.
The process of finding the prime factorization of 44 only has a few differences from the above method of finding the factors of 44. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.
Here are the steps for finding the prime factorization of 44:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 44. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.
Step 2:
Divide 44 by the smallest prime factor, in this case, 2
44 ÷ 2 = 22
2 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 22 as the new focus. Find the smallest prime factor that isn’t 1, and divide 22 by that number. The smallest prime factor you pick for 22 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.
So, the unique prime factors of 44 are: 2, 11
Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
Factors of 57 - The factors of 57 are 1, 3, 19, 57
Factors of 129 - The factors of 129 are 1, 3, 43, 129
Factors of 135 - The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135