# Factors of 214

Factors of 214 are 1, 2, 107, and 214

#### How to find factors of a number

 1.   Find factors of 214 using Division Method 2.   Find factors of 214 using Prime Factorization 3.   Find factors of 214 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 214

• Divide 214 by 1: 214 ÷ 1 : Remainder = 0
• Divide 214 by 2: 214 ÷ 2 : Remainder = 0
• Divide 214 by 107: 214 ÷ 107 : Remainder = 0
• Divide 214 by 214: 214 ÷ 214 : Remainder = 0

Hence, Factors of 214 are 1, 2, 107, and 214

#### 2. Steps to find factors of 214 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 214 using the division method, follow these steps:

• Step 1. Start dividing 214 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 214, which is 2. Divide 214 by 2 to obtain the quotient (107).
214 ÷ 2 = 107
• Step 3. Repeat step 1 with the obtained quotient (107).
107 ÷ 107 = 1

So, the prime factorization of 214 is, 214 = 2 x 107.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 214 as shown below:

So, the prime factorization of 214 is, 214 = 2 x 107.

#### 3. Find factors of 214 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 214 would be the two numbers which, when multiplied, give 214 as the result.

The following table represents the calculation of factors of 214 in pairs:

Factor Pair Pair Factorization
1 and 214 1 x 214 = 214
2 and 107 2 x 107 = 214

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 214. They are called negative pair factors.

Hence, the negative pairs of 214 would be ( -1 , -214 ) , ( -2 , -107 ) .

#### 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. 214 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, 107, 214 are exact divisors of 214.
• 1 is a factor of every number. Eg. 1 is a factor of 214.
• Every number is a factor of zero (0), since 214 x 0 = 0.

• Which is the smallest prime factor of 214?

The smallest prime factor of 214 is 2.

• Is 214 a whole number?

Yes 214 is a whole number.

• What are the prime factors of 214?

The factors of 214 are 1, 2, 107, 214.
Prime factors of 214 are 2, 107.

• What two numbers make 214?

Two numbers that make 214 are 2 and 107.

• What are multiples of 214?

First five multiples of 214 are 428, 642, 856, 1070.

• What is the sum of all factors of 214?

The sum of all factors of 214 is 324.

• What are five multiples of 214?

First five multiples of 214 are 428, 642, 856, 1070, 1284.

• Is 214 a perfect square?

No 214 is not a perfect square.

• What is the greatest prime factors of 214?

The greatest prime factor of 214 is 107.

#### Examples of Factors

How many factors are there for 214?

Factors of 214 are 1, 2, 107, 214.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 214. Can you predict the answer?

3 factor(s) of 214 are 1, 2, 107.

Sammy is puzzled while calculating the prime factors of 214. Can you help him find them?

Factors of 214 are 1, 2, 107, 214.
Prime factors of 214 are 2, 107

What is prime factorization of 214?

Prime factorization of 214 is 2 x 107 = 2 x 107.

Ariel has been assigned the task to find the product of all the prime factors of 214. Can you help her?

Prime factors of 214 are 2, 107.
Hence, the product of prime factors of 214.

Can you help Rubel to find out the product of the even factors of 214?

Factors of 214 are 1, 2, 107, 214.
Even factors of 214 are 2, 214.
Hence, product of even factors of 214 is; 2 x 214 = 428.

Joy wants to calculate mean of all the factors of 214. Help him in finding the mean of 214.

Factors of 214 are 1, 2, 107, 214.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 214 is 1 + 2 + 107 + 214 = 324.
Hence, the mean of factors of 214 is 324 ÷ 4 = 81.00.