1. Steps to find factors of 213 using Division Method

Example: Find factors of 213

  • Divide 213 by 1: 213 ÷ 1 : Remainder = 0
  • Divide 213 by 3: 213 ÷ 3 : Remainder = 0
  • Divide 213 by 71: 213 ÷ 71 : Remainder = 0
  • Divide 213 by 213: 213 ÷ 213 : Remainder = 0

Hence, Factors of 213 are 1, 3, 71, and 213

2. Steps to find factors of 213 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 213 using the division method, follow these steps:

  • Step 1. Start dividing 213 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 213, which is 3. Divide 213 by 3 to obtain the quotient (71).
    213 ÷ 3 = 71
  • Step 3. Repeat step 1 with the obtained quotient (71).
    71 ÷ 71 = 1

So, the prime factorization of 213 is, 213 = 3 x 71.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 213 as shown below:

So, the prime factorization of 213 is, 213 = 3 x 71.

3. Find factors of 213 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 213 would be the two numbers which, when multiplied, give 213 as the result.

The following table represents the calculation of factors of 213 in pairs:

Factor Pair Pair Factorization
1 and 213 1 x 213 = 213
3 and 71 3 x 71 = 213

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 213. They are called negative pair factors.

Hence, the negative pairs of 213 would be ( -1 , -213 ) , ( -3 , -71 ) .

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

  • Every factor of a number is an exact divisor of that number, example 1, 3, 71, 213 are exact divisors of 213.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 213 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 213.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -213 )?

    Factors of -213 are -1, -3, -71, -213.

  • What is the sum of all factors of 213?

    The sum of all factors of 213 is 288.

  • What is prime factorization of 213?

    Prime factorization of 213 is 3 x 71.

  • What are the pair factors of 213?

    Pair factors of 213 are (1,213), (3,71).

  • What are six multiples of 213?

    First five multiples of 213 are 426, 639, 852, 1065, 1278, 1491.

  • Is 213 a whole number?

    Yes 213 is a whole number.

  • Which is the smallest prime factor of 213?

    Smallest prime factor of 213 is 3.

  • What are five multiples of 213?

    First five multiples of 213 are 426, 639, 852, 1065, 1278.

  • Write all factors of 213?

    Factors of 213 are 1, 3, 71, 213.

Examples of Factors

Joey wants to write all the prime factors of 213 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 213 are 3, 71.
So in exponential form it can be written as 3 x 71.

How many factors are there for 213?

Factors of 213 are 1, 3, 71, 213.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 213. Can you predict the answer?

3 factor(s) of 213 are 1, 3, 71.

Sammy is puzzled while calculating the prime factors of 213. Can you help him find them?

Factors of 213 are 1, 3, 71, 213.
Prime factors of 213 are 3, 71

What is prime factorization of 213?

Prime factorization of 213 is 3 x 71 = 3 x 71.

Ariel has been assigned the task to find the product of all the prime factors of 213. Can you help her?

Prime factors of 213 are 3, 71.
Hence, the product of prime factors of 213.

Can you help Rubel to find out the product of the even factors of 213?

Factors of 213 are 1, 3, 71, 213.
Even factors of 213 are 0.
Hence, product of even factors of 213 is; 0 = 0.