# Factors of 1001 in pair

Factors of 1001 in pair are (1, 1001) , (7, 143) , (11, 91) and (13, 77)

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

 1.   Steps to find factors of 1001 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 1001 in pair

Factor Pair Pair Factorization
1 and 1001 1 x 1001 = 1001
7 and 143 7 x 143 = 1001
11 and 91 11 x 91 = 1001
13 and 77 13 x 77 = 1001

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 1001. They are called negative pair factors.

Hence, the negative pairs of 1001 would be ( -1 , -1001 ) .

#### 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 1001 are 1 , 7 , 11 , 13 , 77 , 91 , 143 , 1001. So, factors of 1001 in pair are (1,1001), (7,143), (11,91), (13,77).

#### 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, 7, 11, 13, 77, 91, 143, 1001 are exact divisors of 1001.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1001 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1001.

#### Steps to find Factors of 1001

• Step 1. Find all the numbers that would divide 1001 without leaving any remainder. Starting with the number 1 upto 500 (half of 1001). The number 1 and the number itself are always factors of the given number.
1001 ÷ 1 : Remainder = 0
1001 ÷ 7 : Remainder = 0
1001 ÷ 11 : Remainder = 0
1001 ÷ 13 : Remainder = 0
1001 ÷ 77 : Remainder = 0
1001 ÷ 91 : Remainder = 0
1001 ÷ 143 : Remainder = 0
1001 ÷ 1001 : Remainder = 0

Hence, Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, and 1001

#### Frequently Asked Questions

• Is 1001 a perfect square?

No 1001 is not a perfect square.

• Write five multiples of 1001.

Five multiples of 1001 are 2002, 3003, 4004, 5005, 6006.

• Is there any even prime factor of 1001?

No there is no even prime factor, i.e. 2, of 1001.

• 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.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Can you help Rubel in arranging 1001 blocks in order to form a rectangle in all possible ways? For arranging 1001 blocks in order to form a rectangle in all possible ways we need to find factors of 1001 in pair.

Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001. So, factors of 1001 in pair are (1,1001), (7,143), (11,91), (13,77).

How many total number of factors of 1001 in pair are possible?

Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001. Hence, the factors of 1001 in pair are (1,1001), (7,143), (11,91), (13,77). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 1001 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 1001 are -1, -7, -11, -13, -77, -91, -143, -1001. Hence, factors of 1001 in pair are (-1,-1001), (-7,-143), (-11,-91), (-13,-77).

Find the product of all prime factors of 1001.

Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001. Prime factors are 7, 11, 13. So, the product of all prime factors of 1001 would be 7 x 11 x 13 = 1001.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 1001.
- Writing all prime factors of 1001.
- Writing all the possible factors of 1001 in pair.
Help him in writing all these.

Positive factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001.
Prime factors of 1001 are 7, 11, 13.
Factors of 1001 in pair are (1,1001), (7,143), (11,91), (13,77).

Can you help Sammy list the factors of 1001 and also find the factor pairs?

Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001.
Factors of 1001 in pair are (1,1001), (7,143), (11,91), (13,77).

Help Diji in finding factors of 1001 by Prime Factorization method and then sorting factors of 1001 in pairs.

Prime factorization of 1001 is 7 x 11 x 13. Factors of 1001 in pair can be written as (1,1001), (7,143), (11,91), (13,77).

Write the smallest prime factor of 1001.

Smallest prime factor of 1001 is 7.

Share your expierence with Math-World