# Factors of 50—with division and prime factorization

Contents

## 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,

Factors Of 50 |

1, 2, 5, 10, 25 and 50 |

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.

Links Related to Factors | |

Factors of 15= 1, 3, 5, and 15. | Factor of 36= 1, 2, 3, 4, 6, 9, 12, 18, and 36. |

Factors of 48= 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. | Factors of 18= 1, 2, 3, 6, 9, and 18. |

Factors of 42= 1, 2, 3, 6, 7, 14, 21, and 42. | Factors of 60= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. |

Factors of 35= 1, 5, 7, 35. | Factors of 27= 1, 3, 9, and 27. |

**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