# Factors of 2001

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, and 2001

#### How to find factors of a number

 1.   Find factors of 2001 using Division Method 2.   Find factors of 2001 using Prime Factorization 3.   Find factors of 2001 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2001

• Divide 2001 by 1: 2001 ÷ 1 : Remainder = 0
• Divide 2001 by 3: 2001 ÷ 3 : Remainder = 0
• Divide 2001 by 23: 2001 ÷ 23 : Remainder = 0
• Divide 2001 by 29: 2001 ÷ 29 : Remainder = 0
• Divide 2001 by 69: 2001 ÷ 69 : Remainder = 0
• Divide 2001 by 87: 2001 ÷ 87 : Remainder = 0
• Divide 2001 by 667: 2001 ÷ 667 : Remainder = 0
• Divide 2001 by 2001: 2001 ÷ 2001 : Remainder = 0

Hence, Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, and 2001

#### 2. Steps to find factors of 2001 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 2001 using the division method, follow these steps:

• Step 1. Start dividing 2001 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 2001, which is 3. Divide 2001 by 3 to obtain the quotient (667).
2001 ÷ 3 = 667
• Step 3. Repeat step 1 with the obtained quotient (667).
667 ÷ 23 = 29
29 ÷ 29 = 1

So, the prime factorization of 2001 is, 2001 = 3 x 23 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2001 as shown below:

So, the prime factorization of 2001 is, 2001 = 3 x 23 x 29.

#### 3. Find factors of 2001 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 2001 would be the two numbers which, when multiplied, give 2001 as the result.

The following table represents the calculation of factors of 2001 in pairs:

Factor Pair Pair Factorization
1 and 2001 1 x 2001 = 2001
3 and 667 3 x 667 = 2001
23 and 87 23 x 87 = 2001
29 and 69 29 x 69 = 2001

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 2001. They are called negative pair factors.

Hence, the negative pairs of 2001 would be ( -1 , -2001 ) , ( -3 , -667 ) , ( -23 , -87 ) and ( -29 , -69 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 23, 29, 69, 87, 667, 2001 are exact divisors of 2001.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 2001 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2001.

• What are the prime factors of 2001?

The factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.
Prime factors of 2001 are 3, 23, 29.

• What two numbers make 2001?

Two numbers that make 2001 are 3 and 667.

• What is the greatest prime factors of 2001?

The greatest prime factor of 2001 is 29.

• What are factors of 2001?

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.

• How do you find factors of a negative number? ( eg. -2001 )?

Factors of -2001 are -1, -3, -23, -29, -69, -87, -667, -2001.

• What are five multiples of 2001?

First five multiples of 2001 are 4002, 6003, 8004, 10005, 12006.

• Write some multiples of 2001?

First five multiples of 2001 are 4002, 6003, 8004, 10005.

• Is 2001 a perfect square?

No 2001 is not a perfect square.

• What two numbers make 2001?

Two numbers that make 2001 are 3 and 667.

#### Examples of Factors

What is prime factorization of 2001?

Prime factorization of 2001 is 3 x 23 x 29 = 3 x 23 x 29.

Sammy is puzzled while calculating the prime factors of 2001. Can you help him find them?

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.
Prime factors of 2001 are 3, 23, 29

Kevin has been asked to write 7 factor(s) of 2001. Can you predict the answer?

7 factor(s) of 2001 are 1, 3, 23, 29, 69, 87, 667.

Joey wants to write all the prime factors of 2001 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2001 are 3, 23, 29.
So in exponential form it can be written as 3 x 23 x 29.

How many factors are there for 2001?

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2001? Help her in writing all the factors.

Positive factors are 1, 3, 23, 29, 69, 87, 667, 2001.
Negative factors are -1, -3, -23, -29, -69, -87, -667, -2001.

Can you help Rubel to find out the product of the even factors of 2001?

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.
Even factors of 2001 are 0.
Hence, product of even factors of 2001 is; 0 = 0.