# Factors of 2170

Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, and 2170

#### How to find factors of a number

 1.   Find factors of 2170 using Division Method 2.   Find factors of 2170 using Prime Factorization 3.   Find factors of 2170 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2170

• Divide 2170 by 1: 2170 ÷ 1 : Remainder = 0
• Divide 2170 by 2: 2170 ÷ 2 : Remainder = 0
• Divide 2170 by 5: 2170 ÷ 5 : Remainder = 0
• Divide 2170 by 7: 2170 ÷ 7 : Remainder = 0
• Divide 2170 by 10: 2170 ÷ 10 : Remainder = 0
• Divide 2170 by 14: 2170 ÷ 14 : Remainder = 0
• Divide 2170 by 31: 2170 ÷ 31 : Remainder = 0
• Divide 2170 by 35: 2170 ÷ 35 : Remainder = 0
• Divide 2170 by 62: 2170 ÷ 62 : Remainder = 0
• Divide 2170 by 70: 2170 ÷ 70 : Remainder = 0
• Divide 2170 by 155: 2170 ÷ 155 : Remainder = 0
• Divide 2170 by 217: 2170 ÷ 217 : Remainder = 0
• Divide 2170 by 310: 2170 ÷ 310 : Remainder = 0
• Divide 2170 by 434: 2170 ÷ 434 : Remainder = 0
• Divide 2170 by 1085: 2170 ÷ 1085 : Remainder = 0
• Divide 2170 by 2170: 2170 ÷ 2170 : Remainder = 0

Hence, Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, and 2170

#### 2. Steps to find factors of 2170 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 2170 using the division method, follow these steps:

• Step 1. Start dividing 2170 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 2170, which is 2. Divide 2170 by 2 to obtain the quotient (1085).
2170 ÷ 2 = 1085
• Step 3. Repeat step 1 with the obtained quotient (1085).
1085 ÷ 5 = 217
217 ÷ 7 = 31
31 ÷ 31 = 1

So, the prime factorization of 2170 is, 2170 = 2 x 5 x 7 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2170 as shown below:

So, the prime factorization of 2170 is, 2170 = 2 x 5 x 7 x 31.

#### 3. Find factors of 2170 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 2170 would be the two numbers which, when multiplied, give 2170 as the result.

The following table represents the calculation of factors of 2170 in pairs:

Factor Pair Pair Factorization
1 and 2170 1 x 2170 = 2170
2 and 1085 2 x 1085 = 2170
5 and 434 5 x 434 = 2170
7 and 310 7 x 310 = 2170
10 and 217 10 x 217 = 2170
14 and 155 14 x 155 = 2170
31 and 70 31 x 70 = 2170
35 and 62 35 x 62 = 2170

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 2170. They are called negative pair factors.

Hence, the negative pairs of 2170 would be ( -1 , -2170 ) , ( -2 , -1085 ) , ( -5 , -434 ) , ( -7 , -310 ) , ( -10 , -217 ) , ( -14 , -155 ) , ( -31 , -70 ) and ( -35 , -62 ) .

#### 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. 2170 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, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170 are exact divisors of 2170.
• 1 is a factor of every number. Eg. 1 is a factor of 2170.
• Every number is a factor of zero (0), since 2170 x 0 = 0.

• What are the prime factors of 2170?

The factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.
Prime factors of 2170 are 2, 5, 7, 31.

• What is the sum of all factors of 2170?

The sum of all factors of 2170 is 4608.

• What are the pair factors of 2170?

Pair factors of 2170 are (1,2170), (2,1085), (5,434), (7,310), (10,217), (14,155), (31,70), (35,62).

• What two numbers make 2170?

Two numbers that make 2170 are 2 and 1085.

• What are multiples of 2170?

First five multiples of 2170 are 4340, 6510, 8680, 10850.

• Is 2170 a perfect square?

No 2170 is not a perfect square.

• Which is greatest factor of 2170?

The greatest factor of 2170 is 1085.

• How do you factors of 2170?

Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.

• What are five multiples of 2170?

First five multiples of 2170 are 4340, 6510, 8680, 10850, 13020.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 2170?

Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.
Even factors of 2170 are 2, 10, 14, 62, 70, 310, 434, 2170.
Hence, product of even factors of 2170 is; 2 x 10 x 14 x 62 x 70 x 310 x 434 x 2170 = 354779827360000.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2170? Help her in writing all the factors.

Positive factors are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.
Negative factors are -1, -2, -5, -7, -10, -14, -31, -35, -62, -70, -155, -217, -310, -434, -1085, -2170.

How many factors are there for 2170?

Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.
So there are in total 16 factors.

Sammy is puzzled while calculating the prime factors of 2170. Can you help him find them?

Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.
Prime factors of 2170 are 2, 5, 7, 31

Joey wants to write all the prime factors of 2170 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2170 are 2, 5, 7, 31.
So in exponential form it can be written as 2 x 5 x 7 x 31.

What is prime factorization of 2170?

Prime factorization of 2170 is 2 x 5 x 7 x 31 = 2 x 5 x 7 x 31.

Can you help Rubel to find out the product of the even factors of 2170?

Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.
Even factors of 2170 are 2, 10, 14, 62, 70, 310, 434, 2170.
Hence, product of even factors of 2170 is; 2 x 10 x 14 x 62 x 70 x 310 x 434 x 2170 = 354779827360000.