# Factors of 210

Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210

#### How to find factors of a number

 1.   Find factors of 210 using Division Method 2.   Find factors of 210 using Prime Factorization 3.   Find factors of 210 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 210

• Divide 210 by 1: 210 ÷ 1 : Remainder = 0
• Divide 210 by 2: 210 ÷ 2 : Remainder = 0
• Divide 210 by 3: 210 ÷ 3 : Remainder = 0
• Divide 210 by 5: 210 ÷ 5 : Remainder = 0
• Divide 210 by 6: 210 ÷ 6 : Remainder = 0
• Divide 210 by 7: 210 ÷ 7 : Remainder = 0
• Divide 210 by 10: 210 ÷ 10 : Remainder = 0
• Divide 210 by 14: 210 ÷ 14 : Remainder = 0
• Divide 210 by 15: 210 ÷ 15 : Remainder = 0
• Divide 210 by 21: 210 ÷ 21 : Remainder = 0
• Divide 210 by 30: 210 ÷ 30 : Remainder = 0
• Divide 210 by 35: 210 ÷ 35 : Remainder = 0
• Divide 210 by 42: 210 ÷ 42 : Remainder = 0
• Divide 210 by 70: 210 ÷ 70 : Remainder = 0
• Divide 210 by 105: 210 ÷ 105 : Remainder = 0
• Divide 210 by 210: 210 ÷ 210 : Remainder = 0

Hence, Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210

#### 2. Steps to find factors of 210 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 210 using the division method, follow these steps:

• Step 1. Start dividing 210 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 210, which is 2. Divide 210 by 2 to obtain the quotient (105).
210 ÷ 2 = 105
• Step 3. Repeat step 1 with the obtained quotient (105).
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 210 is, 210 = 2 x 3 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 210 as shown below:

So, the prime factorization of 210 is, 210 = 2 x 3 x 5 x 7.

#### 3. Find factors of 210 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 210 would be the two numbers which, when multiplied, give 210 as the result.

The following table represents the calculation of factors of 210 in pairs:

Factor Pair Pair Factorization
1 and 210 1 x 210 = 210
2 and 105 2 x 105 = 210
3 and 70 3 x 70 = 210
5 and 42 5 x 42 = 210
6 and 35 6 x 35 = 210
7 and 30 7 x 30 = 210
10 and 21 10 x 21 = 210
14 and 15 14 x 15 = 210

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 210. They are called negative pair factors.

Hence, the negative pairs of 210 would be ( -1 , -210 ) , ( -2 , -105 ) , ( -3 , -70 ) , ( -5 , -42 ) , ( -6 , -35 ) , ( -7 , -30 ) , ( -10 , -21 ) and ( -14 , -15 ) .

#### 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. 210 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, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 are exact divisors of 210.
• 1 is a factor of every number. Eg. 1 is a factor of 210.
• Every number is a factor of zero (0), since 210 x 0 = 0.

• What are the prime factors of 210?

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
Prime factors of 210 are 2, 3, 5, 7.

• What two numbers make 210?

Two numbers that make 210 are 2 and 105.

• What is the greatest prime factors of 210?

The greatest prime factor of 210 is 7.

• What are factors of 210?

Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.

• How do you find factors of a negative number? ( eg. -210 )?

Factors of -210 are -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -70, -105, -210.

• What are five multiples of 210?

First five multiples of 210 are 420, 630, 840, 1050, 1260.

• Write some multiples of 210?

First five multiples of 210 are 420, 630, 840, 1050.

• Is 210 a perfect square?

No 210 is not a perfect square.

• What two numbers make 210?

Two numbers that make 210 are 2 and 105.

#### Examples of Factors

What is prime factorization of 210?

Prime factorization of 210 is 2 x 3 x 5 x 7 = 2 x 3 x 5 x 7.

Sammy is puzzled while calculating the prime factors of 210. Can you help him find them?

Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
Prime factors of 210 are 2, 3, 5, 7

Kevin has been asked to write 15 factor(s) of 210. Can you predict the answer?

15 factor(s) of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105.

Joey wants to write all the prime factors of 210 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 210 are 2, 3, 5, 7.
So in exponential form it can be written as 2 x 3 x 5 x 7.

How many factors are there for 210?

Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 210? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
Negative factors are -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -70, -105, -210.

Can you help Rubel to find out the product of the even factors of 210?

Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
Even factors of 210 are 2, 6, 10, 14, 30, 42, 70, 210.
Hence, product of even factors of 210 is; 2 x 6 x 10 x 14 x 30 x 42 x 70 x 210 = 31116960000.