# Factors of 218

Factors of 218 are 1, 2, 109, and 218

#### How to find factors of a number

 1.   Find factors of 218 using Division Method 2.   Find factors of 218 using Prime Factorization 3.   Find factors of 218 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 218

• Divide 218 by 1: 218 ÷ 1 : Remainder = 0
• Divide 218 by 2: 218 ÷ 2 : Remainder = 0
• Divide 218 by 109: 218 ÷ 109 : Remainder = 0
• Divide 218 by 218: 218 ÷ 218 : Remainder = 0

Hence, Factors of 218 are 1, 2, 109, and 218

#### 2. Steps to find factors of 218 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 218 using the division method, follow these steps:

• Step 1. Start dividing 218 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 218, which is 2. Divide 218 by 2 to obtain the quotient (109).
218 ÷ 2 = 109
• Step 3. Repeat step 1 with the obtained quotient (109).
109 ÷ 109 = 1

So, the prime factorization of 218 is, 218 = 2 x 109.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 218 as shown below:

So, the prime factorization of 218 is, 218 = 2 x 109.

#### 3. Find factors of 218 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 218 would be the two numbers which, when multiplied, give 218 as the result.

The following table represents the calculation of factors of 218 in pairs:

Factor Pair Pair Factorization
1 and 218 1 x 218 = 218
2 and 109 2 x 109 = 218

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 218. They are called negative pair factors.

Hence, the negative pairs of 218 would be ( -1 , -218 ) , ( -2 , -109 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 218 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, 109, 218 are exact divisors of 218.
• 1 is a factor of every number. Eg. 1 is a factor of 218.
• Every number is a factor of zero (0), since 218 x 0 = 0.

• What two numbers make 218?

Two numbers that make 218 are 2 and 109.

• What is prime factorization of 218?

Prime factorization of 218 is 2 x 109.

• Write some multiples of 218?

First five multiples of 218 are 436, 654, 872, 1090.

• Which is the smallest prime factor of 218?

The smallest prime factor of 218 is 2.

• Is 218 a perfect square?

No 218 is not a perfect square.

• What is the sum of all factors of 218?

The sum of all factors of 218 is 330.

• What are factors of 218?

Factors of 218 are 1, 2, 109, 218.

• How do you find factors of a negative number? ( eg. -218 )?

Factors of -218 are -1, -2, -109, -218.

• Is 218 a whole number?

Yes 218 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 218. Help him in finding the mean of 218.

Factors of 218 are 1, 2, 109, 218.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 218 is 1 + 2 + 109 + 218 = 330.
Hence, the mean of factors of 218 is 330 ÷ 4 = 82.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 218? Help her in writing all the factors.

Positive factors are 1, 2, 109, 218.
Negative factors are -1, -2, -109, -218.

Joey wants to write all the prime factors of 218 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 218 are 2, 109.
So in exponential form it can be written as 2 x 109.

Kevin has been asked to write 3 factor(s) of 218. Can you predict the answer?

3 factor(s) of 218 are 1, 2, 109.

Sammy is puzzled while calculating the prime factors of 218. Can you help him find them?

Factors of 218 are 1, 2, 109, 218.
Prime factors of 218 are 2, 109

What is prime factorization of 218?

Prime factorization of 218 is 2 x 109 = 2 x 109.

Can you help Rubel to find out the product of the even factors of 218?

Factors of 218 are 1, 2, 109, 218.
Even factors of 218 are 2, 218.
Hence, product of even factors of 218 is; 2 x 218 = 436.