Factors of 224
Like many threedigit even numbers, 224 has several factors, which include 2, 4, 8, 14, and 16. In total there are 12 factors of 224. In this lesson, we will calculate the factors of 224, prime factors of 224, and factors of 224 in pairs along with solved examples for a better understanding.
 Factors of 224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224
 Prime Factorization of 224 : 224 = 2^{5} × 7
What are the Factors of 224?
Factors of 224 are numbers which exactly divide it and gives the remainder as 0. So, when you multiply any two whole numbers with each other and get 224 as the answer you can say that both of those two numbers will be the factors of 224.
For example, you can get 224 as an answer as:
 1 × 224 = 224
 112 × 2 = 224
 32 × 7 = 224
 28 × 8 = 224
 14 × 16 = 224
So in general we can say that "The factors of 224 are all the integers that divide 224 without any remainder."
How to Calculate the Factors of 224?
Factors of 224 are the numbers when multiplied together gives the product as 224.
We can find the factors of 224 by two methods:
 Prime factorization method
 Up side down division method
So, the factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224.
Factors of 224 by Prime Factorization
Prime factorization is a way of expressing a number as a product of its prime factors.
Examples
When we write a number as a product of its factors, we say that the number has been factorized.
Let's see three different ways of factorizing the number 224
Did you observe that we ultimately arrive at only one factorization, that is, 224 = 2 × 2 × 2 × 2 × 2 × 7?
This is a prime factorization of 224.
Look at the alternative way of finding the prime factors of 224
This is the repeated division method and we see the prime factorization of 224 is 224 = 2 × 2 × 2 × 2 × 2 × 7. 2, 7 are the prime factors and we see that 2 is a repeated prime factor.
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 it, for prime numbers, there are no other factors.
Explore factors using illustrations and interactive examples
 Factors of 245  The factors of 245 are 1, 5, 7, 35, 49 and 245
 Factors of 243  The factors of 243 are 1, 3, 9, 27, 81, and 243
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24
 Factors of 225  The factor of 225 are 1, 3, 5, 9, 15, 25, 45, 75 and 225
Challenging Question:
 Find the factors of following number using prime factorization and factor tree method.
a) 2244
b) 222224
c) 224224
Factors of 224 in Pairs
 The factor pairs of 224 are the product of two factors which will always result in 224.
 The Positive factor pairs of 224 are (14,16), (1, 224), (2,112), (4,56), (7,32) and (8,28).
 Product of two negatives is positive. So, the Negative factor pairs of 224 are: (14,16), (1, 224), (2,112), (4,56), (7,32) and (8,28)
Important Notes:
 1 is a common factor of all numbers.
 The factors of a prime number are 1 and the number itself.
 The positive factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224
Factors of 224 Solved Examples

Example 1:
Find the prime factors of 224.
Solution:
Factors of 224: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Prime factorization of 224 is 1 × 2 × 2 × 2 × 2 × 2 × 7 = 2^{5} × 7
Hence, prime factors of 224 are: 1, 2, and 7.
Prime factorization of 224 is 2 × 2 × 2 × 2 × 2 × 7 = 2^{5} × 7 
Example 2:
Jimmy wants to write common factors of 224 and 112.
Solution:
Let's see the factors of 224 and 224
 Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
 Factors of 224: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
Common factors of 112 and 224 are 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112.
FAQs on Factors of 224
What are the factors of 224?
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224
What are the positive pair factors of 224?
The Positive factor pairs of 224 are: (14,16), (1, 224), (2,112), (4,56), (7,32) and (8,28).
What are the negative pair factors of 224?
The negative factor pairs of 224 are: (14,16), (1, 224), (2,112), (4,56), (7,32) and (8,28).
What are the prime factors of 224?
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224
Prime factors of 224 are 1, 2, 7.
What factors of 224 are perfect squares?
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224
4= 2 × 2 and 16 = 4 × 4 are perfect squares.
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