# Factors of 2006 in pair

Factors of 2006 in pair are (1, 2006) , (2, 1003) , (17, 118) and (34, 59)

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

 1.   Steps to find factors of 2006 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 2006 in pair

Factor Pair Pair Factorization
1 and 2006 1 x 2006 = 2006
2 and 1003 2 x 1003 = 2006
17 and 118 17 x 118 = 2006
34 and 59 34 x 59 = 2006

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 2006. They are called negative pair factors.

Hence, the negative pairs of 2006 would be ( -1 , -2006 ) .

#### 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 2006 are 1 , 2 , 17 , 34 , 59 , 118 , 1003 , 2006. So, factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59).

#### 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

• Each number is a factor of itself. Eg. 2006 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, 17, 34, 59, 118, 1003, 2006 are exact divisors of 2006.
• 1 is a factor of every number. Eg. 1 is a factor of 2006.
• Every number is a factor of zero (0), since 2006 x 0 = 0.

#### Steps to find Factors of 2006

• Step 1. Find all the numbers that would divide 2006 without leaving any remainder. Starting with the number 1 upto 1003 (half of 2006). The number 1 and the number itself are always factors of the given number.
2006 ÷ 1 : Remainder = 0
2006 ÷ 2 : Remainder = 0
2006 ÷ 17 : Remainder = 0
2006 ÷ 34 : Remainder = 0
2006 ÷ 59 : Remainder = 0
2006 ÷ 118 : Remainder = 0
2006 ÷ 1003 : Remainder = 0
2006 ÷ 2006 : Remainder = 0

Hence, Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, and 2006

• Is 2006 a composite number?

Yes 2006 is a composite number.

• Is 2006 a prime number?

No 2006 is not a prime number.

• Is 2006 a perfect square?

No 2006 is not a perfect square.

• Write five multiples of 2006.

Five multiples of 2006 are 4012, 6018, 8024, 10030, 12036.

• Write all odd factors of 2006?

The factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006.
Odd factors of 2006 are 1 , 17 , 59 , 1003.

#### Examples of Factors

Can you help Rubel in arranging 2006 blocks in order to form a rectangle in all possible ways? For arranging 2006 blocks in order to form a rectangle in all possible ways we need to find factors of 2006 in pair.

Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. So, factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59).

Ariel has been asked to write all factor pairs of 2006 but she is finding it difficult. Can you help her find out?

Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. So, factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59).

How many total number of factors of 2006 in pair are possible?

Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. Hence, the factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 2006 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 2006 are -1, -2, -17, -34, -59, -118, -1003, -2006. Hence, factors of 2006 in pair are (-1,-2006), (-2,-1003), (-17,-118), (-34,-59).

Help Deep in writing the positive factors of 2006 in pair and negative factor of 2006 in pair.

Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. Positive factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59). Negative factors of 2006 in pair are (-1,-2006), (-2,-1003), (-17,-118), (-34,-59).

Find the product of all factors of 2006.

Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. So the product of all factors of 2006 would be 1 x 2 x 17 x 34 x 59 x 118 x 1003 x 2006 = 16192865729296.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 2006.
- Writing all prime factors of 2006.
- Writing all the possible factors of 2006 in pair.
Help him in writing all these.

Positive factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006.
Prime factors of 2006 are 2, 17, 59.
Factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59).

Can you help Sammy list the factors of 2006 and also find the factor pairs?

Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006.
Factors of 2006 in pair are (1,2006), (2,1003), (17,118), (34,59).