# Factors of 2002

Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, and 2002

#### How to find factors of a number

 1.   Find factors of 2002 using Division Method 2.   Find factors of 2002 using Prime Factorization 3.   Find factors of 2002 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2002

• Divide 2002 by 1: 2002 ÷ 1 : Remainder = 0
• Divide 2002 by 2: 2002 ÷ 2 : Remainder = 0
• Divide 2002 by 7: 2002 ÷ 7 : Remainder = 0
• Divide 2002 by 11: 2002 ÷ 11 : Remainder = 0
• Divide 2002 by 13: 2002 ÷ 13 : Remainder = 0
• Divide 2002 by 14: 2002 ÷ 14 : Remainder = 0
• Divide 2002 by 22: 2002 ÷ 22 : Remainder = 0
• Divide 2002 by 26: 2002 ÷ 26 : Remainder = 0
• Divide 2002 by 77: 2002 ÷ 77 : Remainder = 0
• Divide 2002 by 91: 2002 ÷ 91 : Remainder = 0
• Divide 2002 by 143: 2002 ÷ 143 : Remainder = 0
• Divide 2002 by 154: 2002 ÷ 154 : Remainder = 0
• Divide 2002 by 182: 2002 ÷ 182 : Remainder = 0
• Divide 2002 by 286: 2002 ÷ 286 : Remainder = 0
• Divide 2002 by 1001: 2002 ÷ 1001 : Remainder = 0
• Divide 2002 by 2002: 2002 ÷ 2002 : Remainder = 0

Hence, Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, and 2002

#### 2. Steps to find factors of 2002 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 2002 using the division method, follow these steps:

• Step 1. Start dividing 2002 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 2002, which is 2. Divide 2002 by 2 to obtain the quotient (1001).
2002 ÷ 2 = 1001
• Step 3. Repeat step 1 with the obtained quotient (1001).
1001 ÷ 7 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1

So, the prime factorization of 2002 is, 2002 = 2 x 7 x 11 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2002 as shown below:

So, the prime factorization of 2002 is, 2002 = 2 x 7 x 11 x 13.

#### 3. Find factors of 2002 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 2002 would be the two numbers which, when multiplied, give 2002 as the result.

The following table represents the calculation of factors of 2002 in pairs:

Factor Pair Pair Factorization
1 and 2002 1 x 2002 = 2002
2 and 1001 2 x 1001 = 2002
7 and 286 7 x 286 = 2002
11 and 182 11 x 182 = 2002
13 and 154 13 x 154 = 2002
14 and 143 14 x 143 = 2002
22 and 91 22 x 91 = 2002
26 and 77 26 x 77 = 2002

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 2002. They are called negative pair factors.

Hence, the negative pairs of 2002 would be ( -1 , -2002 ) , ( -2 , -1001 ) , ( -7 , -286 ) , ( -11 , -182 ) , ( -13 , -154 ) , ( -14 , -143 ) , ( -22 , -91 ) and ( -26 , -77 ) .

#### 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. 2002 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, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002 are exact divisors of 2002.
• 1 is a factor of every number. Eg. 1 is a factor of 2002.
• Every number is a factor of zero (0), since 2002 x 0 = 0.

• Is 2002 a perfect square?

No 2002 is not a perfect square.

• What are factors of 2002?

Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.

• Which is greatest factor of 2002?

The greatest factor of 2002 is 1001.

• What is the sum of all factors of 2002?

The sum of all factors of 2002 is 4032.

• What are multiples of 2002?

First five multiples of 2002 are 4004, 6006, 8008, 10010.

• What is the greatest prime factors of 2002?

The greatest prime factor of 2002 is 13.

• What are six multiples of 2002?

First five multiples of 2002 are 4004, 6006, 8008, 10010, 12012, 14014.

• What is prime factorization of 2002?

Prime factorization of 2002 is 2 x 7 x 11 x 13.

• Is 2002 a whole number?

Yes 2002 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2002? Help her in writing all the factors.

Positive factors are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.
Negative factors are -1, -2, -7, -11, -13, -14, -22, -26, -77, -91, -143, -154, -182, -286, -1001, -2002.

Can you help Sammy find out the product of the odd factors of 2002?

Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.
Odd factors of 2002 are 1, 7, 11, 13, 77, 91, 143, 1001.
Hence product of odd factors of 2002 is; 1 x 7 x 11 x 13 x 77 x 91 x 143 x 1001 = 1004006004001.

Joey wants to write all the prime factors of 2002 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2002 are 2, 7, 11, 13.
So in exponential form it can be written as 2 x 7 x 11 x 13.

How many factors are there for 2002?

Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 2002. Can you predict the answer?

15 factor(s) of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001.

Sammy is puzzled while calculating the prime factors of 2002. Can you help him find them?

Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002.
Prime factors of 2002 are 2, 7, 11, 13

What is prime factorization of 2002?

Prime factorization of 2002 is 2 x 7 x 11 x 13 = 2 x 7 x 11 x 13.