# Factors of 2010

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, and 2010

#### How to find factors of a number

 1.   Find factors of 2010 using Division Method 2.   Find factors of 2010 using Prime Factorization 3.   Find factors of 2010 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2010

• Divide 2010 by 1: 2010 ÷ 1 : Remainder = 0
• Divide 2010 by 2: 2010 ÷ 2 : Remainder = 0
• Divide 2010 by 3: 2010 ÷ 3 : Remainder = 0
• Divide 2010 by 5: 2010 ÷ 5 : Remainder = 0
• Divide 2010 by 6: 2010 ÷ 6 : Remainder = 0
• Divide 2010 by 10: 2010 ÷ 10 : Remainder = 0
• Divide 2010 by 15: 2010 ÷ 15 : Remainder = 0
• Divide 2010 by 30: 2010 ÷ 30 : Remainder = 0
• Divide 2010 by 67: 2010 ÷ 67 : Remainder = 0
• Divide 2010 by 134: 2010 ÷ 134 : Remainder = 0
• Divide 2010 by 201: 2010 ÷ 201 : Remainder = 0
• Divide 2010 by 335: 2010 ÷ 335 : Remainder = 0
• Divide 2010 by 402: 2010 ÷ 402 : Remainder = 0
• Divide 2010 by 670: 2010 ÷ 670 : Remainder = 0
• Divide 2010 by 1005: 2010 ÷ 1005 : Remainder = 0
• Divide 2010 by 2010: 2010 ÷ 2010 : Remainder = 0

Hence, Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, and 2010

#### 2. Steps to find factors of 2010 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 2010 using the division method, follow these steps:

• Step 1. Start dividing 2010 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 2010, which is 2. Divide 2010 by 2 to obtain the quotient (1005).
2010 ÷ 2 = 1005
• Step 3. Repeat step 1 with the obtained quotient (1005).
1005 ÷ 3 = 335
335 ÷ 5 = 67
67 ÷ 67 = 1

So, the prime factorization of 2010 is, 2010 = 2 x 3 x 5 x 67.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2010 as shown below:

So, the prime factorization of 2010 is, 2010 = 2 x 3 x 5 x 67.

#### 3. Find factors of 2010 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 2010 would be the two numbers which, when multiplied, give 2010 as the result.

The following table represents the calculation of factors of 2010 in pairs:

Factor Pair Pair Factorization
1 and 2010 1 x 2010 = 2010
2 and 1005 2 x 1005 = 2010
3 and 670 3 x 670 = 2010
5 and 402 5 x 402 = 2010
6 and 335 6 x 335 = 2010
10 and 201 10 x 201 = 2010
15 and 134 15 x 134 = 2010
30 and 67 30 x 67 = 2010

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 2010. They are called negative pair factors.

Hence, the negative pairs of 2010 would be ( -1 , -2010 ) , ( -2 , -1005 ) , ( -3 , -670 ) , ( -5 , -402 ) , ( -6 , -335 ) , ( -10 , -201 ) , ( -15 , -134 ) and ( -30 , -67 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 2010 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, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010 are exact divisors of 2010.
• 1 is a factor of every number. Eg. 1 is a factor of 2010.
• Every number is a factor of zero (0), since 2010 x 0 = 0.

• What are the prime factors of 2010?

The factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
Prime factors of 2010 are 2, 3, 5, 67.

• What two numbers make 2010?

Two numbers that make 2010 are 2 and 1005.

• What is the greatest prime factors of 2010?

The greatest prime factor of 2010 is 67.

• What are factors of 2010?

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.

• How do you find factors of a negative number? ( eg. -2010 )?

Factors of -2010 are -1, -2, -3, -5, -6, -10, -15, -30, -67, -134, -201, -335, -402, -670, -1005, -2010.

• What are five multiples of 2010?

First five multiples of 2010 are 4020, 6030, 8040, 10050, 12060.

• Write some multiples of 2010?

First five multiples of 2010 are 4020, 6030, 8040, 10050.

• Is 2010 a perfect square?

No 2010 is not a perfect square.

• What two numbers make 2010?

Two numbers that make 2010 are 2 and 1005.

#### Examples of Factors

What is prime factorization of 2010?

Prime factorization of 2010 is 2 x 3 x 5 x 67 = 2 x 3 x 5 x 67.

Sammy is puzzled while calculating the prime factors of 2010. Can you help him find them?

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
Prime factors of 2010 are 2, 3, 5, 67

Kevin has been asked to write 15 factor(s) of 2010. Can you predict the answer?

15 factor(s) of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005.

Joey wants to write all the prime factors of 2010 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2010 are 2, 3, 5, 67.
So in exponential form it can be written as 2 x 3 x 5 x 67.

How many factors are there for 2010?

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2010? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
Negative factors are -1, -2, -3, -5, -6, -10, -15, -30, -67, -134, -201, -335, -402, -670, -1005, -2010.

Can you help Rubel to find out the product of the even factors of 2010?

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
Even factors of 2010 are 2, 6, 10, 30, 134, 402, 670, 2010.
Hence, product of even factors of 2010 is; 2 x 6 x 10 x 30 x 134 x 402 x 670 x 2010 = 261158528160000.