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Factors of 250: Prime Factorization, Methods, and Examples

The factors of 250 are numbers that produce 250 when two numbers are multiplied together. These numbers also give zero as a remainder. The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 250

Here are the factors of number 250.

Factors of 2501, 2, 5, 10, 25, 50, 125, and 250

Negative Factors of 250

The negative factors of 250 are similar to its positive factors, just with a negative sign.

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

Prime Factorization of 250

The prime factorization of 250 is the way of expressing its prime factors in the product form.

Prime Factorization = 2 x 5$^{3}$

In this article, we will learn about the factors of 250 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 250?

The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250. All of these numbers are the factors as they do not leave any remainder when divided by 250.

The factors of 250 are classified as prime numbers and composite numbers. The prime factors of the number 250 can be determined using the prime factorization technique.

How To Find the Factors of 250?

You can find the factors of 250 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 250, create a list containing the numbers divisible by 250 with zero remainders. One important thing to note is that 1 and 250 are the 250’s factors, as every natural number has one and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 250 are determined as follows:

\[\dfrac{250}{1} = 250\]

\[\dfrac{250}{2} = 125\]

\[\dfrac{250}{5} = 50\]

\[\dfrac{250}{10} = 25\]

Therefore, 1, 2, 5, 10, 25, 50, 125, and 250 are the factors of 250. The whole number quotients of these factors also act as factors of 250.

Total Number of Factors of 250

For 250, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 250. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization of the given number.
  2. Demonstrate the prime factorization of the number in the exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 250 is given as:

Factorization = 1 x 2 x 5$^{3}$

The exponent of 1 and 2 is one, and the exponent of 5 is 3.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 250 is 16. 8 are positive, and eight are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The number factors cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has two as its prime factor, the smallest prime factor.

Factors of 250 by Prime Factorization

The number 250 is a composite number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 250 using prime factorization, let us determine what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 250, divide by its smallest prime factor. First, determine that the given number is either even or odd. Two will be the smallest prime factor if it is an even number.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 250 can be expressed as:

250 = 2 x 5$^{3}$

Factors of 250 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors.

For 250, the factor pairs can be found as:

1 x 250 = 250

2 x 125 = 250 

5 x 50 = 250

10 x 25 = 250

The possible factor pairs of 250 are given as (1, 250), (2, 125), (5, 50), and (10, 25).

All these numbers in pairs, when multiplied, give 250 as the product.

The negative factor pairs of 250 are given as:

-1 x -250 = 250 

-2 x -125 = 250

-5 x -50 = 250

-10 x -25 = 250

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -5, -10, -25, -50, -125 and -250 are called negative factors of 250.

The list of all the factors of 250, including positive and negative numbers, is given below.

Factor list of 250: 1, -1, 2, -2, 5, -5, 10, -10, 25, -25, 50, -50, 125, -125, 250 and -250

Factors of 250 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 250 are there?

Solution

The total number of Factors of 250 is 8.

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

Example 2

Find the factors of 250 using prime factorization.

Solution

The prime factorization of 250 is given as:

 250 $\div$ 2 = 125

125 $\div$ 5 = 25 

25 $\div$ 5 = 5

5 $\div4 5 =1

So the prime factorization of 250 can be written as:

250 = 2 x 5$^{3}$

Factors of 249|Factors List| Factors of 251

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