250 is an even number and must be a factor of 2. Looking at the number in the units place, i.e. 0, we can also find that 5 and 10 are its factors. In this lesson, let us learn to find the other factors of 250. While the list may appear long, it"s fairly simple to remember especially when you identify the pair factors of 250 or look at the factor tree of 250.

You are watching: What is the prime factorization of 250

**Factors of 250:**1, 2, 5, 10, 25, 50, 125 and 250

**Prime Factorization of 250:**2 × 5 × 5 × 5

1. | What Are the Factors of 250? |

2. | How to Calculate Factors of 250? |

3. | Factors of 250 by Prime Factorization |

4. | Factors of 250 in Pairs |

5. | FAQs-on-Factors-of-250 |

Factors of 250 are all the numbers which on multiplying give the value 250. 250 is an even composite number.

250 is a multiple of 2, 5 and 10. Thus 2, 5, 10 are the factors of 250. Let"s find which all numbers multiply together to form 250.

**The factors of 250 are integers that divide 250 without any remainder.**

**Explore factors using illustrations and interactive examples**

Prime factorization means to express a composite number as the product of its prime factors.

To get the prime factorization of 250, we divide it by its smallest prime factor which is 2**250 ÷ 2 = 125Now divide 125 by its smallest prime factor.125 ÷ 5 = 25This process goes on till we get the quotient as 1.25 ÷ 5 = 5 and 5 ÷ 5 = 1The prime factorization of 245 is shown below in 2 ways:**

We stop the factor tree as we cannot branch further because 2 and 5 are the prime numbers. Therefore, the prime factorization of 250 is 2 x 5 x 5 x 5.

These 4 prime factors can be multiplied in pairs in all the possible ways to get the factors of 250.

## Factors of 250 in Pairs

Now that we are familiar with the factors of 250, let"s write factors of 250 in pairs.

The factor-pairs of 250 are (1, 250), (2, 125), (5, 50), (25, 10).

It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

So, we can have negative factor-pairs of 250 as (-1,-250), (-2,-125), (-5,-50), (-25, -10)

Annie is given 2 numbers, 10 and 250. She is provided with a few cards numbered 1, 2, 5, 10, 25, and 50. Can you help her in listing the common factors of 10 and 250?

**Solution: **

The factors of 10 are 1, 2, 5, and 10.

The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.

The common factors of 50 and 250 are 1, 2, 5, and 10.

**Example 2:**Jane bought a rectangular carpet for the living room of her house. The area of the carpet is about 250 square feet. What are the possible dimensions of the carpet?

**Solution:**

The area of a rectangle is length × breadth sq units.

Given area = 250 square feet

So the possible length and breadth are the factor pairs that give the product 250.

Length of carpet (in ft)Breadth of carpet (in ft)1 | 250 |

2 | 125 |

5 | 50 |

10 | 25 |

25 | 10 |

50 | 5 |

250 | 1 |

Therefore, there are 7 possible dimensions of the carpet.

### What are the factors of 250?

The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.

### What are all the factors of 250 and 300?

The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300.

### Is 250 a perfect cube?

The cube root of 250 is not an integer, and therefore 250 is not a perfect cube.

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### How many factors of 250 are there?

The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250. We have 8 factors of 250.