# Factors of 224

Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224

#### How to find factors of a number

 1.   Find factors of 224 using Division Method 2.   Find factors of 224 using Prime Factorization 3.   Find factors of 224 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 224

• Divide 224 by 1: 224 ÷ 1 : Remainder = 0
• Divide 224 by 2: 224 ÷ 2 : Remainder = 0
• Divide 224 by 4: 224 ÷ 4 : Remainder = 0
• Divide 224 by 7: 224 ÷ 7 : Remainder = 0
• Divide 224 by 8: 224 ÷ 8 : Remainder = 0
• Divide 224 by 14: 224 ÷ 14 : Remainder = 0
• Divide 224 by 16: 224 ÷ 16 : Remainder = 0
• Divide 224 by 28: 224 ÷ 28 : Remainder = 0
• Divide 224 by 32: 224 ÷ 32 : Remainder = 0
• Divide 224 by 56: 224 ÷ 56 : Remainder = 0
• Divide 224 by 112: 224 ÷ 112 : Remainder = 0
• Divide 224 by 224: 224 ÷ 224 : Remainder = 0

Hence, Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224

#### 2. Steps to find factors of 224 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 224 using the division method, follow these steps:

• Step 1. Start dividing 224 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 224, which is 2. Divide 224 by 2 to obtain the quotient (112).
224 ÷ 2 = 112
• Step 3. Repeat step 1 with the obtained quotient (112).
112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1

So, the prime factorization of 224 is, 224 = 2 x 2 x 2 x 2 x 2 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 224 as shown below:

So, the prime factorization of 224 is, 224 = 2 x 2 x 2 x 2 x 2 x 7.

#### 3. Find factors of 224 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 224 would be the two numbers which, when multiplied, give 224 as the result.

The following table represents the calculation of factors of 224 in pairs:

Factor Pair Pair Factorization
1 and 224 1 x 224 = 224
2 and 112 2 x 112 = 224
4 and 56 4 x 56 = 224
7 and 32 7 x 32 = 224
8 and 28 8 x 28 = 224
14 and 16 14 x 16 = 224

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 224. They are called negative pair factors.

Hence, the negative pairs of 224 would be ( -1 , -224 ) , ( -2 , -112 ) , ( -4 , -56 ) , ( -7 , -32 ) , ( -8 , -28 ) and ( -14 , -16 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 224 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 224.
• Every number is a factor of zero (0), since 224 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224 are exact divisors of 224.
• Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. Each factor divides 224 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224 are all less than or equal to 224.

• What is prime factorization of 224?

Prime factorization of 224 is 2 x 2 x 2 x 2 x 2 x 7.

• How do you find factors of a negative number? ( eg. -224 )?

Factors of -224 are -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -112, -224.

• What are the prime factors of 224?

The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Prime factors of 224 are 2, 2, 2, 2, 2, 7.

• What are pair factors of 224?

The pair factors of 224 are (1,224), (2,112), (4,56), (7,32), (8,28), (14,16).

• What is the greatest prime factors of 224?

The greatest prime factor of 224 is 7.

• What are six multiples of 224?

First five multiples of 224 are 448, 672, 896, 1120, 1344, 1568.

• What are factors of 224?

Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.

• Which is the smallest prime factor of 224?

Smallest prime factor of 224 is 2.

• Is 224 a whole number?

Yes 224 is a whole number.

#### Examples of Factors

Kevin has been asked to write 11 factor(s) of 224. Can you predict the answer?

11 factor(s) of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112.

Sammy is puzzled while calculating the prime factors of 224. Can you help him find them?

Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Prime factors of 224 are 2, 2, 2, 2, 2, 7

What is prime factorization of 224?

Prime factorization of 224 is 2 x 2 x 2 x 2 x 2 x 7 = 25 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 224. Can you help her?

Prime factors of 224 are 2, 2, 2, 2, 2, 7.
Hence, the product of prime factors of 14.

Can you help Rubel to find out the product of the even factors of 224?

Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Even factors of 224 are 2, 4, 8, 14, 16, 28, 32, 56, 112, 224.
Hence, product of even factors of 224 is; 2 x 4 x 8 x 14 x 16 x 28 x 32 x 56 x 112 x 224 = 18046378835968.

Joy wants to calculate mean of all the factors of 224. Help him in finding the mean of 224.

Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 224 is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 56 + 112 + 224 = 504.
Hence, the mean of factors of 224 is 504 ÷ 12 = 42.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 224? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -112, -224.