# Factors of 212

Factors of 212 are 1, 2, 4, 53, 106, and 212

#### How to find factors of a number

 1.   Find factors of 212 using Division Method 2.   Find factors of 212 using Prime Factorization 3.   Find factors of 212 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 212

• Divide 212 by 1: 212 ÷ 1 : Remainder = 0
• Divide 212 by 2: 212 ÷ 2 : Remainder = 0
• Divide 212 by 4: 212 ÷ 4 : Remainder = 0
• Divide 212 by 53: 212 ÷ 53 : Remainder = 0
• Divide 212 by 106: 212 ÷ 106 : Remainder = 0
• Divide 212 by 212: 212 ÷ 212 : Remainder = 0

Hence, Factors of 212 are 1, 2, 4, 53, 106, and 212

#### 2. Steps to find factors of 212 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 212 using the division method, follow these steps:

• Step 1. Start dividing 212 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 212, which is 2. Divide 212 by 2 to obtain the quotient (106).
212 ÷ 2 = 106
• Step 3. Repeat step 1 with the obtained quotient (106).
106 ÷ 2 = 53
53 ÷ 53 = 1

So, the prime factorization of 212 is, 212 = 2 x 2 x 53.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 212 as shown below:

So, the prime factorization of 212 is, 212 = 2 x 2 x 53.

#### 3. Find factors of 212 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 212 would be the two numbers which, when multiplied, give 212 as the result.

The following table represents the calculation of factors of 212 in pairs:

Factor Pair Pair Factorization
1 and 212 1 x 212 = 212
2 and 106 2 x 106 = 212
4 and 53 4 x 53 = 212

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 212. They are called negative pair factors.

Hence, the negative pairs of 212 would be ( -1 , -212 ) , ( -2 , -106 ) and ( -4 , -53 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 212 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 212.
• Every number is a factor of zero (0), since 212 x 0 = 0.
• 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, 4, 53, 106, 212 are exact divisors of 212.
• Factors of 212 are 1, 2, 4, 53, 106, 212. Each factor divides 212 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 53, 106, 212 are all less than or equal to 212.

• What are the pair factors of 212?

Pair factors of 212 are (1,212), (2,106), (4,53).

• What are five multiples of 212?

First five multiples of 212 are 424, 636, 848, 1060, 1272.

• What two numbers make 212?

Two numbers that make 212 are 2 and 106.

• What is the sum of all factors of 212?

The sum of all factors of 212 is 378.

• What are factors of -212?

Factors of -212 are -1, -2, -4, -53, -106, -212.

• What are factors of 212?

Factors of 212 are 1, 2, 4, 53, 106, 212.

• Is 212 a perfect square?

No 212 is not a perfect square.

• Which is the smallest prime factor of 212?

Smallest prime factor of 212 is 2.

• Which is greatest factor of 212?

The greatest factor of 212 is 106.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 212?

Factors of 212 are 1, 2, 4, 53, 106, 212.
Odd factors of 212 are 1, 53.
Hence product of odd factors of 212 is; 1 x 53 = 53.

Joey wants to write all the prime factors of 212 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 212 are 2, 2, 53.
So in exponential form it can be written as 22 x 53.

How many factors are there for 212?

Factors of 212 are 1, 2, 4, 53, 106, 212.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 212. Can you predict the answer?

5 factor(s) of 212 are 1, 2, 4, 53, 106.

Sammy is puzzled while calculating the prime factors of 212. Can you help him find them?

Factors of 212 are 1, 2, 4, 53, 106, 212.
Prime factors of 212 are 2, 2, 53

What is prime factorization of 212?

Prime factorization of 212 is 2 x 2 x 53 = 22 x 53.

Can you help Rubel to find out the product of the even factors of 212?

Factors of 212 are 1, 2, 4, 53, 106, 212.
Even factors of 212 are 2, 4, 106, 212.
Hence, product of even factors of 212 is; 2 x 4 x 106 x 212 = 179776.