# Factors of 2012

Factors of 2012 are 1, 2, 4, 503, 1006, and 2012

#### How to find factors of a number

 1.   Find factors of 2012 using Division Method 2.   Find factors of 2012 using Prime Factorization 3.   Find factors of 2012 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2012

• Divide 2012 by 1: 2012 ÷ 1 : Remainder = 0
• Divide 2012 by 2: 2012 ÷ 2 : Remainder = 0
• Divide 2012 by 4: 2012 ÷ 4 : Remainder = 0
• Divide 2012 by 503: 2012 ÷ 503 : Remainder = 0
• Divide 2012 by 1006: 2012 ÷ 1006 : Remainder = 0
• Divide 2012 by 2012: 2012 ÷ 2012 : Remainder = 0

Hence, Factors of 2012 are 1, 2, 4, 503, 1006, and 2012

#### 2. Steps to find factors of 2012 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 2012 using the division method, follow these steps:

• Step 1. Start dividing 2012 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 2012, which is 2. Divide 2012 by 2 to obtain the quotient (1006).
2012 ÷ 2 = 1006
• Step 3. Repeat step 1 with the obtained quotient (1006).
1006 ÷ 2 = 503
503 ÷ 503 = 1

So, the prime factorization of 2012 is, 2012 = 2 x 2 x 503.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2012 as shown below:

So, the prime factorization of 2012 is, 2012 = 2 x 2 x 503.

#### 3. Find factors of 2012 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 2012 would be the two numbers which, when multiplied, give 2012 as the result.

The following table represents the calculation of factors of 2012 in pairs:

Factor Pair Pair Factorization
1 and 2012 1 x 2012 = 2012
2 and 1006 2 x 1006 = 2012
4 and 503 4 x 503 = 2012

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 2012. They are called negative pair factors.

Hence, the negative pairs of 2012 would be ( -1 , -2012 ) , ( -2 , -1006 ) and ( -4 , -503 ) .

#### 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. 2012 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2012.
• Every number is a factor of zero (0), since 2012 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, 503, 1006, 2012 are exact divisors of 2012.
• Factors of 2012 are 1, 2, 4, 503, 1006, 2012. Each factor divides 2012 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 503, 1006, 2012 are all less than or equal to 2012.

• What are the pair factors of 2012?

Pair factors of 2012 are (1,2012), (2,1006), (4,503).

• What are five multiples of 2012?

First five multiples of 2012 are 4024, 6036, 8048, 10060, 12072.

• What two numbers make 2012?

Two numbers that make 2012 are 2 and 1006.

• What is the sum of all factors of 2012?

The sum of all factors of 2012 is 3528.

• What are factors of -2012?

Factors of -2012 are -1, -2, -4, -503, -1006, -2012.

• What are factors of 2012?

Factors of 2012 are 1, 2, 4, 503, 1006, 2012.

• Is 2012 a perfect square?

No 2012 is not a perfect square.

• Which is the smallest prime factor of 2012?

Smallest prime factor of 2012 is 2.

• Which is greatest factor of 2012?

The greatest factor of 2012 is 1006.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 2012?

Factors of 2012 are 1, 2, 4, 503, 1006, 2012.
Odd factors of 2012 are 1, 503.
Hence product of odd factors of 2012 is; 1 x 503 = 503.

Joey wants to write all the prime factors of 2012 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2012 are 2, 2, 503.
So in exponential form it can be written as 22 x 503.

How many factors are there for 2012?

Factors of 2012 are 1, 2, 4, 503, 1006, 2012.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 2012. Can you predict the answer?

5 factor(s) of 2012 are 1, 2, 4, 503, 1006.

Sammy is puzzled while calculating the prime factors of 2012. Can you help him find them?

Factors of 2012 are 1, 2, 4, 503, 1006, 2012.
Prime factors of 2012 are 2, 2, 503

What is prime factorization of 2012?

Prime factorization of 2012 is 2 x 2 x 503 = 22 x 503.

Can you help Rubel to find out the product of the even factors of 2012?

Factors of 2012 are 1, 2, 4, 503, 1006, 2012.
Even factors of 2012 are 2, 4, 1006, 2012.
Hence, product of even factors of 2012 is; 2 x 4 x 1006 x 2012 = 16192576.