# Factors of 254

Factors of 254 are 1, 2, 127, and 254

#### How to find factors of a number

 1.   Find factors of 254 using Division Method 2.   Find factors of 254 using Prime Factorization 3.   Find factors of 254 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 254

• Divide 254 by 1: 254 ÷ 1 : Remainder = 0
• Divide 254 by 2: 254 ÷ 2 : Remainder = 0
• Divide 254 by 127: 254 ÷ 127 : Remainder = 0
• Divide 254 by 254: 254 ÷ 254 : Remainder = 0

Hence, Factors of 254 are 1, 2, 127, and 254

#### 2. Steps to find factors of 254 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 254 using the division method, follow these steps:

• Step 1. Start dividing 254 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 254, which is 2. Divide 254 by 2 to obtain the quotient (127).
254 ÷ 2 = 127
• Step 3. Repeat step 1 with the obtained quotient (127).
127 ÷ 127 = 1

So, the prime factorization of 254 is, 254 = 2 x 127.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 254 as shown below:

So, the prime factorization of 254 is, 254 = 2 x 127.

#### 3. Find factors of 254 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 254 would be the two numbers which, when multiplied, give 254 as the result.

The following table represents the calculation of factors of 254 in pairs:

Factor Pair Pair Factorization
1 and 254 1 x 254 = 254
2 and 127 2 x 127 = 254

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 254. They are called negative pair factors.

Hence, the negative pairs of 254 would be ( -1 , -254 ) , ( -2 , -127 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 254 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 127, 254 are exact divisors of 254.
• 1 is a factor of every number. Eg. 1 is a factor of 254.
• Every number is a factor of zero (0), since 254 x 0 = 0.

• What two numbers make 254?

Two numbers that make 254 are 2 and 127.

• What is prime factorization of 254?

Prime factorization of 254 is 2 x 127.

• Write some multiples of 254?

First five multiples of 254 are 508, 762, 1016, 1270.

• Which is the smallest prime factor of 254?

The smallest prime factor of 254 is 2.

• Is 254 a perfect square?

No 254 is not a perfect square.

• What is the sum of all factors of 254?

The sum of all factors of 254 is 384.

• What are factors of 254?

Factors of 254 are 1, 2, 127, 254.

• How do you find factors of a negative number? ( eg. -254 )?

Factors of -254 are -1, -2, -127, -254.

• Is 254 a whole number?

Yes 254 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 254. Help him in finding the mean of 254.

Factors of 254 are 1, 2, 127, 254.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 254 is 1 + 2 + 127 + 254 = 384.
Hence, the mean of factors of 254 is 384 ÷ 4 = 96.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 254? Help her in writing all the factors.

Positive factors are 1, 2, 127, 254.
Negative factors are -1, -2, -127, -254.

Joey wants to write all the prime factors of 254 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 254 are 2, 127.
So in exponential form it can be written as 2 x 127.

Kevin has been asked to write 3 factor(s) of 254. Can you predict the answer?

3 factor(s) of 254 are 1, 2, 127.

Sammy is puzzled while calculating the prime factors of 254. Can you help him find them?

Factors of 254 are 1, 2, 127, 254.
Prime factors of 254 are 2, 127

What is prime factorization of 254?

Prime factorization of 254 is 2 x 127 = 2 x 127.

Can you help Rubel to find out the product of the even factors of 254?

Factors of 254 are 1, 2, 127, 254.
Even factors of 254 are 2, 254.
Hence, product of even factors of 254 is; 2 x 254 = 508.