Factors of 448: Prime Factorization, Methods, and Examples

Like every other number, the number 448 has both positive and negative factors. The list of integers that completely divide 448 i.e. does not leave any remainder are said to be the factors of 448. 

When they divide 448 the quotient is also an integer rather than a decimal number.

Factors of 448

Here are the factors of number 448.

Factors of 448: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224 and 448

Negative Factors of 448

The negative factors of 448 are similar to its positive aspects, just with a negative sign.

Negative Factors of 448: -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -64, -112, -224 and -448

Prime Factorization of 448

The prime factorization of 448 is the way of expressing its prime factors in the product form.

Prime Factorization: 2$^6$ x 7

In this article, we will learn about the factors of 448 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 448?

The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224 and 448. These numbers are the factors as they do not leave any remainder when divided by 448.

The factors of 448 are classified as prime numbers and composite numbers. The prime factors of the number 448 can be determined using the prime factorization technique.

How To Find the Factors of 448?

You can find the factors of 448 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 448, create a list containing the numbers that are exactly divisible by 448 with zero remainders. One important thing to note is that 1 and 448 are the 448’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 448 are determined as follows:

\[\dfrac{448}{1} = 448\]

\[\dfrac{448}{2} = 224\]

\[\dfrac{448}{4} = 112\]

\[\dfrac{448}{7} = 64\]

\[\dfrac{448}{8} = 56\]

\[\dfrac{448}{14} = 32\]

\[\dfrac{448}{16} = 28\]

\[\dfrac{448}{28} = 16\]

\[\dfrac{448}{32} = 14\]

\[\dfrac{448}{56} = 8\]

\[\dfrac{448}{64} = 7\]

\[\dfrac{448}{112} = 4\]

\[\dfrac{448}{224} = 2\]

\[\dfrac{448}{448} = 1\]

Therefore, 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224 and 448 are the factors of 448.

Total Number of Factors of 448

For 448, there are 14 positive factors and 14 negative ones. So in total, there are 28 factors of 448. 

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 448 is given as:

Factorization of 448 is 1 x 2$^6$ x 7.

The exponent of 2 is 6 whereas the exponent of 1 and 7 is 1.

Adding 1 to each and multiplying them together results in m.

Therefore, the total number of factors of 448 is 28. 14 are positive, and 14 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 448 by Prime Factorization

The number 448 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 448 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 448, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 448 can be expressed as:

448 = 2 x 2 x 2 x 2 x 2 x 2 x 7

Factors of  in Pairs 448

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 448, the factor pairs can be found as:

1 x 448 = 448

2 x 224 = 448

4 x 112 = 448

7 x 64 = 448

8 x 56 = 448

14 x 32 = 448

16 x 28 = 448

The possible factor pairs of 448 are given as (1, 448), (2, 224), (4, 112), (7, 64), (8, 56),(14, 32) and (16, 28).

All these numbers in pairs, when multiplied, give 448 as the product.

The negative factor pairs of 448 are given as:

-1 x -448 = 448

-2 x -224 = 448

-4 x -112 = 448

-7 x -64 = 448

-8 x -56 = 448

-14 x -32 = 448

-16 x -28 = 448

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -64, -112, -224 and -448 are called negative factors of 448.

The list of all the factors of 448, including positive as well as negative numbers, is given below.

Factor list of 448: 1, -1, 2, -2, 4, -4, 7, -7, 8, -8, 14, -14, 16, -16, 28, -28 32, -32, 56, -56, 64, -64, 112, -112, 224, -224, 448 and -448

Factors of 448 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 448 are there?

Solution

The total number of Factors of 448 is 14.

Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224 and 448

Example 2

Find the factors of 448 using prime factorization.

Solution

The prime factorization of 448 is given as:

448 $\div$ 2 = 224 

224 $\div$ 2 = 112

112 $\div$ 2 = 56

56 $\div$ 2 = 28

28 $\div$ 2 = 14

14 $\div$ 2 = 7 

7 $\div$ 7 = 1     

So the prime factorization of 448 can be written as:

2$^2$ x 7 = 448

Factors of 447|Factors List| Factors of 449