Maths How To with Anita

# What is the prime factorization of 254?

Are you struggling to find the prime factorization of 254 and other numbers? You’re not alone.

As a high school math teacher for over 14 years I love helping students make math fun and easy.

When you’re trying to multiply or divide something, the factors involved are important. That’s why I wrote this article – to help make learning about and understanding factors easier than ever.

I want you to feel confident in your skills so that you can take on every problem with confidence.

Read on to learn fun and easy methods to find the prime factorization of 254.

## What are the factors of 254?

The factors of 254 are 1, 2, 127 & 254.

Factors are whole numbers that divide into 254 exactly with no remainder.

## What is the prime factorization of 254?

The prime factorization of 254 can be written as 2 x 127.

This means that the prime factors of 254 are 2 and 127.

## How to find the prime factors of 254

You can use a variety of methods to find the prime factors of 254 including repeated division, drawing a factor tree, using a calculator or the divisibility tests and drawing factor rainbows to find factor pairs.

### Repeated division

You can use repeated division to find the prime factorization of 254.

Here’s how:

1) Start by dividing 254 by the smallest prime number greater than 1, which is 2.

2) Continue dividing by 2 until you get a number that is not divisible by 2. In this case, it’s 127.

4) Now, divide 127 by the next prime number, which is 3.

5) Continue dividing 127 by the next prime numbers, 5, 7, 11, 13, etc until you get a whole number as the answer.

6) Since 127 can not be divided any further as it is a prime number, you now have your prime factorization of 254 = 2 x 127.

### Draw a factor tree

Another way to find the prime factorization of 254 is to draw a factor tree.

Here’s how:

1) Write down the number you want to find the prime factorization of, in this case 254, and draw two lines (branches) underneath it.

2) Find two factors of 254 and write them down under the branches, putting a circle around any prime numbers.

3) Continue adding branches under any composite factors, however in this case there aren’t any. This is when you know you can stop.

4) The prime factorization is then the product of the prime numbers that are circled in your factor tree.

## Factor tree for 254

Here is the factor tree for 254.

## How to find the factors of 254

Finding the factors of a number is a useful skill to consolidate your understanding of multiplication and division as well as for other math topics such as fractions and algebra.

There are a variety of methods to find the factors of 254 including using a calculator, using the divisibility tests and drawing a factor rainbow.

### Using a calculator

With a simple scientific calculator, simply enter 254 and press the division button to find what whole numbers you can divide 254 by without any remainder. This will give you the factors of 254.

Of these factors, if they are prime numbers then they are called prime factors of 254.

## Using the divisibility rules

The divisibility rules are a set of simple tests that you can use to quickly find the factors of 254.

Here are the divisibility rules:

– A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.

– A number is divisible by 3 if the sum of all the digits is divisible by 3.

– A number is divisible by 4 if the last two digits are divisible by 4.

– A number is divisible by 5 if the last digit is 0 or 5.

– A number is divisible by 6 if the number is divisible by both 2 and 3.

– A number is divisible by 9 if the sum of all the digits is divisible by 9.

– A number is divisible by 10 if the last digit is 0.

So using these rules,

– 254 is divisible by 2 since the last digit is 4, an even number.

– 254 is not divisible by 3 since the sum of all the digits is 11 which is not divisible by 3.

– 254 is not divisible by 4 since the last two digits, 54, is not divisible by 4.

– 254 is not divisible by 5 since the last digit is not 0 or 5.

– 254 is not divisible by 6 since it is not divisible by both 2 and 3.

– 254 is not divisible by 9 since the sum of all the digits is 11 which is divisible by 9.

– 254 is not divisible by 10 since the last digit is not 0.

## What are the factors pairs of 254

Factor pairs are 2 numbers that multiply together to equal 254.

They are:

1 x 254 = 254

2 x 127 = 254

Here is a factor rainbow for 254:

## What is the product of prime factors of 254?

The product of prime factors of 254 is 2 x 127

## Negative factors of 254

The negative factors of 254 are -1, -2, -127 & -254.

Since 2 negative numbers multiply together to equal a positive number, both numbers must be negative.

For example

-1 x -254 = 254

-2 x -127 = 254

## FAQs

### How many factors are there for 254?

254 has 4 factors; 1,2,127 & 254

Yes