# Factors of 50—with division and prime factorization ## Factors Of 50

In mathematics, factors of 50 are numbers that divide 50 completely and without leaving any remainder.

There are always more than two factors in composite numbers.

Here, we will use a simple multiplication method to find factors of the number 50. The multiples of 50 are 50, 100, 150, 200, 250, 300, 350, 400, 450 and so on.

## How to Calculate Factors of 50?

In order to find the factors of 50, we must check the natural numbers from 1 to 50. We must divide 50 evenly or completely in order to find the factors.

50 ÷ 1 = 50

50 ÷ 2 = 25

50 ÷ 5 = 10

50 ÷ 10 = 5

50 ÷ 25 = 2

50 ÷ 50 = 1

## What are Factors of -50?

When we multiply two numbers, and we get -50 as a product, that numbers are the factors of -50.

Here is the explanation:

-1 × 50 = -50

1 × -50 = -50

-2 × 25 = -50

2 × -25 = -50

-5 × 10 = -50

5 × -10 = -50

We can get -50 by having (-1, 50), (-2, 25), and(-5, 10) as a pair of factors. Similarly, we can also get -50 by having (1, -50), (2, -25), and(5, -10) as a pair of factors.

## Factors Of 50 in Pairs

By multiplying two numbers in a pair, we can find the factors of number 50, such as;

1 × 50 = 50

2 × 25 = 50

5 × 10 = 50

Therefore,

To get the original number, we can also write the negative pair factors as the product of two:

-1 × -50 = 50

-2 × -25 = 50

-5 × -10 = 50

## Prime Factorization of 50

In mathematics, the number 50 is a composite number. We will now find prime factors of 50.

Step 01:

• In the first step, divide 50 by the smallest prime factor, i.e. 2.

50 ÷ 2 = 25

Step 02:

• When we divide 25 by 2, we get a fractional number of 12.5, which is not considered a factor.

Step 03:

• Next, we will take a look at 3 and 5, and so on and so forth

3 is not a factor of 50, so 25 × 3 = 8.33

Step 04:

• Take 25 and divide it by 5.

25 ÷ 5 = 5

Therefore, 5 is a factor of 50.

Step 05:

• Using the same method as before, we get the following results:

5 ÷ 5 = 1

Step 06:

• In addition, we received a 1 at the end, and therefore we cannot use the division method. The prime factors of 50 are 2 × 5 × 5 or 2 × 52, where 2 and 5 are prime numbers.

## Solved Examples

Q.1: If there are 50 erasers distributed equally in 5 boxes. What is the total number of pencils?

Solution:

Given,

Number of erasers = 50

Number of boxes = 5

Number of erasers in each box = 50/5 = 10

Q.2: If the price of one apple is Rs. 5, then what is the cost of 10 apples?

Solution:

Price of one apple = Rs. 5

Price of 10 apples = 10 × 5 = Rs. 50

Q.3: What are the common factors of 50 and 100?

Solution:

Factors of 50 are 1, 2, 5, 10, 25, and 50

As we know, 50 × 2 = 100

Since all the factors of 50 are factors of 100, except for 100 itself, every factor of 50 is a factor of 100.

As a result, 50 and 100 have the common factors 1,2,5,10,25, and 50.

## FAQs

### What are the factors of 50?

Natural numbers are the factors of 50 that divide the original number evenly. These are 1,2,5,10,25 and 50.

### Are the factors, and multiples of 50, same or different?

Multiples of 50 are different from factors of 50. A factor divides the original number into equal parts, whereas a multiple is the product form of a number if it is multiplied by several natural numbers.

### What are the multiples of 50 in Maths?

The first ten multiples of 50 are 50, 100, 150, 200, 250, 300, 350, 400, 450 and 500.

### Which is the highest prime factor of 50?

The prime factorization of 50 reveals that 50 = 2 × 5 × 5. Thus, 5 is the greatest prime factor.

### What are common factors of 50, 125, and 150?

Factors of 50 = 1, 2, 5, 10, 25, 50

Factors of 125 = 1, 5, 25, 125

Factors of 175 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Hence, the common factors of 50, 125 and 175 = 1, 5 and 25