# Factors of 250 — Easy division and prime factorization

Contents

## Factors of 250

**In Mathematics, factors of 250 are the natural numbers by which the original number can be evenly divided.**

They are also called divisors of 250 since they divide the original number. Although 250 is a multiple of 25, it is not a perfect square. Moreover, 250 is divisible by 5 (by divisibility rules).

When the multiplication of two natural numbers equals 250, they are the necessary factors of 250. A composite number with an even number factor is 250.

Let’s identify the factors of 250 as well as the prime and pair factors.

**What are Factors of -250?**

When we multiply two numbers, and we get -250 as a product, that numbers are the factors of -250.

Here is the explanation:

-1 × 250 = -250

1 × -250 = -250

-2 × 125 = -250

2 × -125 = -250

-5 × 50 = -250

5 × -50 = -250

-10 × 25 = -250

10 × -25 = -250

We can get -250 by having (-1, 250), (-2, 125), (-5, 50), and (-10, 25) as a pair of factors. Similarly, we can also get -250 by having(1, -250), (2, -125), (5, -50), and (10, -25) as a pair of factors.

**How to Find the Factors of 250?**

Finding the factors of 250 is easy. In order to divide 250 evenly, we must divide it by all such natural numbers. Alternatively, you can multiply these two numbers together to get 250.

Division Method | Multiplication Method |

250 ÷ 1 = 250 | 1 × 250 = 250 |

250 ÷ 2 = 125 | 2 × 125 = 250 |

250 ÷ 5 = 50 | 5 × 50 = 250 |

250 ÷ 10 = 25 | 10 × 25 = 250 |

250 ÷ 25 = 10 | 25 × 10 = 250 |

250 ÷ 50 = 5 | 50 × 5 = 250 |

250 ÷ 225 = 2 | 225 × 5 = 250 |

250 ÷ 250 = 1 | 250 × 1 = 250 |

Thus, the factors of 250 are **1, 2, 5, 10, 25, 50, 125, 250.**

**More Factors**

**Factors of 215 = **1, 5, 43 and 215.

**Factors of 216 = **1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.

**Factors of 415 = ** 1, 5, 83 and 415.

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

**Factors of 144 = **1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.

**Factors of 120 = **1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

**Pair Factors of 250**

When two integers are multiplied by each other to result in 250, then they have required pair factors. Then,

1 × 250 = 250

2 × 125 = 250

5 × 50 = 250

10 × 25 = 250

Thus, the pair factors of 250 are **(1, 250), (2, 125), (5, 50), and (10, 25).**

To get the factors in pairs, we can find the product of two negative numbers:

-1 × -250 = 250

-2 × -125 = 250

-5 × -50 = 250

-10 × -25 = 250

Thus, the **negative pair factors **are (-1, -250), (-2, -125), (-5, -50), (-10, -25).

**Prime Factorization of 250**

If we prime factorize 250, we will get prime factors that divide the original number evenly.

Dividing 250 by the smallest prime number | 250 ÷ 2 = 125 |

Again, dividing 125 by the smallest prime number | 125 ÷ 5 = 25 |

Dividing 25 by 5 | 25 ÷ 5 = 5 |

Again, dividing 5 by 5 | 5 ÷ 5 = 1 |

Therefore, the prime factors of 250 are 2 and 5.

Prime factorization of 250 = 2 × 5 × 5 × 5Exponential form = 21 x 53 |

Links Related to Factors | |

Multiples of 24 in pairs= 1, 2, 3, 4, 6, 8, 12, and 24. | Factors 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. |

Multiples of 46 in pairs= 1, 2, 23, and 46. | Factors of 72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. |

Factors of 84= 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84. | Multiples of 441 in pairs= 1, 3, 7, 9, 21, 49, 63, 147, and 441. |

**Solved Examples**

**Q.1: How much is the sum of all the factors of 250?**

**Solution**: Factors of 250 = 1, 2, 5, 10, 25, 50, 125, 250.

Sum = 1+2+5+10+25+50+125+ 250 = 468

Thus, the required sum is 468.

**Q.2: Calculate the common factors of 255 and 250.**

**Solution**: Let us look at the factors of the numbers 255 and 250.

250 = 1, 2, 5, 10, 25, 50, 125, 250

255 = 1, 3, 5, 15, 17, 51, 85, 255

Thus, the common factors of 250 and 255 are 1 and 5.

**Q.3: Find out the GCF of 250 and 260.**

**Solution**: The individual factors are:

250 = 1, 2, 5, 10, 25, 50, 125, 250

260 = 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260

Thus, the greatest common factor between 250 and 260 is:

GCF (250, 260) = 10

**Practice Questions**

- Find the average of factors of 250.
- Find the common factors of 250 and 150.
- Is 20 a factor of 250?
- Write the factors of 250 in product form.
- Sheena wants to distribute 250 chocolates among 50 children in a classroom. How can she do that?

**FAQ’s**

### What are the factors of 250?

Factors of 250 = 1, 2, 5, 10, 25, 50, 125, 250.

### What are the prime factors of 250?

There are only two prime factors that divide 250, namely 2 and 5.

### Is 250 a composite number?

Yes, 250 is a composite number since it contains more than two factors.

### What are the multiples of 250?

250, 500, 750, 1000, 1250, 1500, 1750, 2000, 2250, 2500 are multiples of 250.

### What is the GCF of 150 and 250?

Here are the respective factors:

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

250 = 1, 2, 5, 10, 25, 50, 125, 250

GCF (150, 250) = 50

Here are the respective factors:

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

250 = 1, 2, 5, 10, 25, 50, 125, 250

GCF (150, 250) = 50