# Factors of 2010 in pair

Factors of 2010 in pair are (1, 2010) , (2, 1005) , (3, 670) , (5, 402) , (6, 335) , (10, 201) , (15, 134) and (30, 67)

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

 1.   Steps to find factors of 2010 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 2010 in pair

Factor Pair Pair Factorization
1 and 2010 1 x 2010 = 2010
2 and 1005 2 x 1005 = 2010
3 and 670 3 x 670 = 2010
5 and 402 5 x 402 = 2010
6 and 335 6 x 335 = 2010
10 and 201 10 x 201 = 2010
15 and 134 15 x 134 = 2010
30 and 67 30 x 67 = 2010

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 2010. They are called negative pair factors.

Hence, the negative pairs of 2010 would be ( -1 , -2010 ) .

#### Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 2010 are 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 , 67 , 134 , 201 , 335 , 402 , 670 , 1005 , 2010. So, factors of 2010 in pair are (1,2010), (2,1005), (3,670), (5,402), (6,335), (10,201), (15,134), (30,67).

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 2010 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, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010 are exact divisors of 2010.
• 1 is a factor of every number. Eg. 1 is a factor of 2010.
• Every number is a factor of zero (0), since 2010 x 0 = 0.

#### Steps to find Factors of 2010

• Step 1. Find all the numbers that would divide 2010 without leaving any remainder. Starting with the number 1 upto 1005 (half of 2010). The number 1 and the number itself are always factors of the given number.
2010 ÷ 1 : Remainder = 0
2010 ÷ 2 : Remainder = 0
2010 ÷ 3 : Remainder = 0
2010 ÷ 5 : Remainder = 0
2010 ÷ 6 : Remainder = 0
2010 ÷ 10 : Remainder = 0
2010 ÷ 15 : Remainder = 0
2010 ÷ 30 : Remainder = 0
2010 ÷ 67 : Remainder = 0
2010 ÷ 134 : Remainder = 0
2010 ÷ 201 : Remainder = 0
2010 ÷ 335 : Remainder = 0
2010 ÷ 402 : Remainder = 0
2010 ÷ 670 : Remainder = 0
2010 ÷ 1005 : Remainder = 0
2010 ÷ 2010 : Remainder = 0

Hence, Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, and 2010

• Is 2010 a composite number?

Yes 2010 is a composite number.

• Is 2010 a prime number?

No 2010 is not a prime number.

• What is the mean of factors of 2010?

Factors of 2010 are 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 , 67 , 134 , 201 , 335 , 402 , 670 , 1005 , 2010. therefore mean of factors of 2010 is (1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 67 + 134 + 201 + 335 + 402 + 670 + 1005 + 2010) / 16 = 306.00.

• 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

Ariel has been asked to write all factor pairs of 2010 but she is finding it difficult. Can you help her find out?

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. So, factors of 2010 in pair are (1,2010), (2,1005), (3,670), (5,402), (6,335), (10,201), (15,134), (30,67).

Sammy wants to write all the negative factors of 2010 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 2010 are -1, -2, -3, -5, -6, -10, -15, -30, -67, -134, -201, -335, -402, -670, -1005, -2010. Hence, factors of 2010 in pair are (-1,-2010), (-2,-1005), (-3,-670), (-5,-402), (-6,-335), (-10,-201), (-15,-134), (-30,-67).

Help Deep in writing the positive factors of 2010 in pair and negative factor of 2010 in pair.

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. Positive factors of 2010 in pair are (1,2010), (2,1005), (3,670), (5,402), (6,335), (10,201), (15,134), (30,67). Negative factors of 2010 in pair are (-1,-2010), (-2,-1005), (-3,-670), (-5,-402), (-6,-335), (-10,-201), (-15,-134), (-30,-67).

Find the product of all prime factors of 2010.

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. Prime factors are 2, 3, 5, 67. So, the product of all prime factors of 2010 would be 2 x 3 x 5 x 67 = 2010.

Can you help Sammy list the factors of 2010 and also find the factor pairs?

Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
Factors of 2010 in pair are (1,2010), (2,1005), (3,670), (5,402), (6,335), (10,201), (15,134), (30,67).

Help Diji in finding factors of 2010 by Prime Factorization method and then sorting factors of 2010 in pairs.

Prime factorization of 2010 is 2 x 3 x 5 x 67. Factors of 2010 in pair can be written as (1,2010), (2,1005), (3,670), (5,402), (6,335), (10,201), (15,134), (30,67).

Write the smallest prime factor of 2010.

Smallest prime factor of 2010 is 2.

Write the largest prime factor of 2010.

Largest prime factor of 2010 is 67.