# Factors of 2001 in pair

Factors of 2001 in pair are (1, 2001) , (3, 667) , (23, 87) and (29, 69)

#### How to find factors of a number in pair

 1.   Steps to find factors of 2001 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 2001 in pair

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 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 2001 are 1 , 3 , 23 , 29 , 69 , 87 , 667 , 2001. So, factors of 2001 in pair are (1,2001), (3,667), (23,87), (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.

#### Steps to find Factors of 2001

• Step 1. Find all the numbers that would divide 2001 without leaving any remainder. Starting with the number 1 upto 1000 (half of 2001). The number 1 and the number itself are always factors of the given number.
2001 ÷ 1 : Remainder = 0
2001 ÷ 3 : Remainder = 0
2001 ÷ 23 : Remainder = 0
2001 ÷ 29 : Remainder = 0
2001 ÷ 69 : Remainder = 0
2001 ÷ 87 : Remainder = 0
2001 ÷ 667 : Remainder = 0
2001 ÷ 2001 : Remainder = 0

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

• Is 2001 a composite number?

Yes 2001 is a composite number.

• Is 2001 a perfect square?

No 2001 is not a perfect square.

• Write all odd factors of 2001?

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

• What is the mean of all prime factors of 2001?

Factors of 2001 are 1 , 3 , 23 , 29 , 69 , 87 , 667 , 2001. Prime factors of 2001 are 3 , 23 , 29. Therefore mean of prime factors of 2001 is (3 + 23 + 29) / 3 = 18.33.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

#### Examples of Factors

Can you help Rubel in arranging 2001 blocks in order to form a rectangle in all possible ways? For arranging 2001 blocks in order to form a rectangle in all possible ways we need to find factors of 2001 in pair.

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001. So, factors of 2001 in pair are (1,2001), (3,667), (23,87), (29,69).

How many total number of factors of 2001 in pair are possible?

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001. Hence, the factors of 2001 in pair are (1,2001), (3,667), (23,87), (29,69). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 2001 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 2001 are -1, -3, -23, -29, -69, -87, -667, -2001. Hence, factors of 2001 in pair are (-1,-2001), (-3,-667), (-23,-87), (-29,-69).

Find the product of all prime factors of 2001.

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001. Prime factors are 3, 23, 29. So, the product of all prime factors of 2001 would be 3 x 23 x 29 = 2001.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 2001.
- Writing all prime factors of 2001.
- Writing all the possible factors of 2001 in pair.
Help him in writing all these.

Positive factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.
Prime factors of 2001 are 3, 23, 29.
Factors of 2001 in pair are (1,2001), (3,667), (23,87), (29,69).

Can you help Sammy list the factors of 2001 and also find the factor pairs?

Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001.
Factors of 2001 in pair are (1,2001), (3,667), (23,87), (29,69).

Help Diji in finding factors of 2001 by Prime Factorization method and then sorting factors of 2001 in pairs.

Prime factorization of 2001 is 3 x 23 x 29. Factors of 2001 in pair can be written as (1,2001), (3,667), (23,87), (29,69).

Write the smallest prime factor of 2001.

Smallest prime factor of 2001 is 3.