# Factors of 448—with division and prime factorization

## Factors of 448

Factors of 448 are the integer that can be divided equally into 448

Overall, there are 14 factors that contribute to 448, of which 448 is the most important, and its prime factors are 2, 7. The total factor count of 448 is 1016.

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

Prime Factors of 448: 2, 7

Prime Factorization of 448: 26 × 71

Sum of Factors of 448: 1016

## What are the Factors of 448?

Pairs of numbers whose products equal 448 are called factors of 448. These factors can either be prime numbers or composite numbers.

## What are Factors of -448?

When we multiply two numbers, and we get -448 as a product, that numbers are the factors of -448.

Here is the explanation:

-1 × 448 = -448

1 × -448 = -448

-2 × 224 = -448

2 × -224 = -448

-4 × 112 = -448

4 × 112 = -448

-7 × 64 = -448

7 × -64 = -448

-8 × 56 = -448

8 × -56 = -448

-14 × 32 = -448

14 × -32 = -448

-16 × 28 = -448

16 × -28 = -448

We can get -448 by having (-1, 448), (-2, 224), (-4, 112), (-7, 64), (-8, 56), (-14, 32), and (-16, 28) as a pair of factors. Similarly, we can also get -448 by having (1, -448), (2, -224), (4, -112), (7, -64), (8, -56), (14, -32), and (16, -28)as a pair of factors.

## How to Find the Factors of 448?

If we want to find the factors of 448, we need to find the numbers that divide 448 without leaving any remainder.

• 448/112 = 4; therefore, 112 is a factor of 448, and also 4 is a factor of 448.
• 448/56 = 8; therefore, 56 is a factor of 4, and 8 also is a factor of 4.

In the same way, we can find other factors. Hence, the factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.

• Factors of 180—The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
• Factors of 25—The factors of 25 are 1, 5, 25
• Factors of 33—The factors of 33 are 1, 3, 11, 33
• Factors of 100—The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
• Factors of 40—The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

## Factors of 448 by Prime Factorization

As a composite number, 448 will have prime factors. We will now look at how to calculate the prime factors of 448. The first step is to divide the number 448 by the smallest prime factor, 2. Divide until there is no zero remainder.

448 ÷ 2 = 224

224 ÷ 2 = 112

112 ÷ 2 = 56

56 ÷ 2 = 28

28 ÷ 2 = 14

14 ÷ 2 = 7

Additionally, dividing 7 by 2 leaves a non-zero remainder. Therefore, we stop the process and divide the number 7 by the next smallest prime factor. When we reach the end of the prime factor or cannot divide further, we stop.

So, the prime factorization of 448 is 26 × 71 where 2, 7 are prime.

## Factors of 448 in Pairs

The pair factors of 448 are the numbers that, when multiplied, equal the number 448. The factors of 448 in pairs as follows:

1 × 448 = (1, 448)

2 × 224 = (2, 224)

4 × 112 = (4, 112)

7 × 64 = (7, 64)

8 × 56 = (8, 56)

14 × 32 = (14, 32)

16 × 28 = (16, 28)

448 has the following negative pair factors:

-1 × -448 = (-1, -448)

-2 × -224 = (-2, -224)

-4 × -112 = (-4, -112)

-7 × -64 = (-7, -64)

-8 × -56 = (-8, -56)

-14 × -32 = (-14, -32)

-16 × -28 = (-16, -28)

NOTE: If (a, b) is the pair factor of a number, then (b, a) is also the pair factor of that number.

## Solved Examples

1. Example 1: What are the factors that make up 448?
Solution:
Since 448 has too many factors, if we are able to determine the prime factorization of 448, we can calculate the total number of factors using the formula below.
If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 448 = 26 × 71
Hence, the total number of factors are (6 + 1) × (1 + 1) = 7 × 2 = 14
2. Example 2: Find out the Least Common Multiple and Greatest Common Divisor (GCD) of 448 and 232.
Solution:
Factors of 448 = 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 Factors of 232 = 1, 2, 4, 8, 29, 58, 116, 232.

Hence, the Least Common Multiple of 448 and 232 is 12992 and Greatest Common Divisor (GCD) of 448 and 232 is 8.
3. Example 3: Determine whether 1, 2, 4, 28, 32, 92, 112 and 448 are factors of 448.
Solution:
A remainder is left over when we divide 448 by 92. This means that 92 is not a factor of 448. Every other number is a factor of 448, except for 92.
4. Example 4: Calculate the product of all the prime factors of 448.
Solution:
Since, the prime factors of 448 are 2, 7. Thus, the product of prime factors = 2 × 7 = 14.

## FAQs

### What are the Factors of 448?

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

Negative factors of 448 = -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -64, -112, -224, -448.

### What is the Sum of the Factors of 448?

The sum of all factors of 448 = (26 + 1 – 1)/(2 – 1) × (71 + 1 – 1)/(7 – 1) = 1016

### What are Prime Factors of 448?

448 has the factors 2, 7 as its prime factors.

### What is the Greatest Common Factor of 448 and 44?

Factors of 448 and 44 are respectively 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 and 1, 2, 4, 11, 22, 44.

Common factors of 448 and 44 are [1, 2, 4].

Therefore, the Greatest Common Factor of 448 and 44 is 4.

### What are the Common Factors of 448 and 416?

Since,

Factors of 448 = 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 and the Factors of 416 = 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.

Therefore, [1, 2, 4, 8, 16, 32] are the common factors of 448 and 416.