Factors of 210
Did you know that 210 is the only number that is divisible by all the numbers from 1 to 7 (except 4) without leaving any remainder? Try it yourself. In fact, you may discover that if you multiply the three consecutive numbers 5, 6, and 7, it will also give 210 as the answer!
In this lesson, we will calculate the factors of 210, prime factors of 210, and factors of 210 in pairs along with solved examples for a better understanding.
 Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105 and 210
 Prime Factorization of 210: 210 = 2 × 3 × 5 × 7
1.  What Are the Factors of 210? 
2.  How to Calculate the Factors of 210? 
3.  Factors of 210 by Prime Factorization 
4.  Factors of 210 in Pairs 
5.  Important Notes 
6.  FAQs on Factors of 210 
What Are the Factors of 210?
Factors of 210 will be those numbers that exactly divide it and give the remainder as 0. For instance, when you multiply any two whole numbers with each other and get 210 as the answer, you can say that those two numbers will be the factors of 210. For example, you can get 210 as the result for:
 1 × 210 = 210
 2 × 105 = 210
 3 × 70 = 210
 5 × 42 = 210
 6 × 35 = 210
 7 × 30 = 210
 10 × 21 = 210
 14 × 15 = 210
This can be continued until you reach 210 × 1 = 210. Thus, in general, we can say that the factors of 210 are all the integers that 210 can be divided into.
How to Calculate the Factors of 210?
Let's begin calculating the factors of 210, starting with the smallest whole number i.e. 1. Divide 210 with this number. Is the remainder 0? Yes! So, we will get:
 210 ÷ 1 = 210
 210 × 1 = 210
The next whole number is 2. Now divide 210 with this number.
 210 ÷ 2 = 105
 2 × 105 = 210
Proceeding in a similar manner we get,
 1 × 210 = 210
 2 ×105 = 210
 3 × 70 = 210
 5 × 42 = 210
Explore factors using illustrations and interactive examples
 Factors of 121  The factors of 121 are 1, 11, and 121.
 Factors of 125  The factors of 125 are 1, 5, 25, and 125.
 Factors of 128  The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
 Factors of 112  The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
 Factors of 512  The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
 Factors of 20  The factors of 1, 2, 4, 5, 10, and 20.
Factors of 210 by Prime Factorization
Prime factorization means to express a composite number as the product of its prime factors. To get the prime factorization of 210, we will divide it by its smallest prime factor which is 2.
 210 ÷ 2 = 105
Now, 105 is divided by its smallest prime factor and the quotient is obtained. This process goes on till we get the quotient as 1. The prime factorization of 210 is shown below.
Now that we have done the prime factorization of our number, we can multiply the numbers and get the other factors of 210. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.
Factors of 210 in Pairs
The pairs of numbers which give 210 when multiplied are known as the factor pairs of 210. The following are the factors of 210 in pairs:
Product form of 210  Pair factor 
1 × 210 = 210 × 1 = 210  (1,210) 
2 × 105 = 105 × 2 = 210  (2,105) 
3 × 70 = 70 × 3 = 210  (3,70) 
5 × 42 = 42 × 5 = 210  (5,42) 
6 × 35 = 35 × 6 = 210  (6,35) 
7 × 30 = 30 × 7 = 210  (7,30) 
10 × 21 = 21 × 10 = 210  (10,21) 
14 × 15 = 15 × 14 = 210  (14,15) 
Observe in the table above, after 14 × 15, the factors start repeating, except that they are in a different order. Thus, it is enough to find factors till (14,15).
 If we consider negative integers, then both the numbers in the pair factors have to be negative.
 We know that  ve (×)  ve = +ve.
 Thus, we can have factor pairs of 210 as (1,210); (2,105); (3,70). and so on.
Important Notes:
 Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
 1 is a universal factor.
 The two numbers that are multiplied to give a product are the factors of the product.
 As 210 ends with digit 0, it will have 5 and 10 as its factors. This holds true for any number that ends with digit 0.
 210 is a nonperfect square number. Thus, it will have an even number of factors. This property holds true for every nonperfect square number.
Think Tank:
 Are 0.1 and 2100 factors of 210? Why do you think so?
Factors of 210 Solved Examples

Example 1: Robert's teacher told him that (3) is one of the factors of 210. Can you help him find the other factor?
Solution:
210 = Factor 1 × Factor 2
210 = (3) × Factor 2
Factor 2 = 210 ÷ (3) = 70
Thus, the other factor is 70. 
Example 2: Peter and Andrew have rectangular carpets in their respective rooms with dimensions as shown below:
a) 15 inches x 14 inches
b) 21 inches x 10 inchesThey place the two carpets one over another. Since the two of them do not overlap, Peter said that they don't have the same area. However, Andrew does not agree with him. Can you find out who is correct?
Solution:
Area of a rectangle = length × breadth
For the first carpet, Area = 14 × 15 = 210 in^{2}.
For the second carpet, Area = 10 × 21 = 210 in^{2}.
Thus, they have equal areas.
FAQs on Factors of 210
What are the factors of 210?
All the factors of 210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
What is the prime factorization of 210?
The prime factorization of 210 is obtained by dividing 210 by all its prime factors until we get the quotient as 1.
Thus, 210 = 2 × 3 × 5 × 7 is the prime factorization.
What are all the negative pair factors of 210?
The negative pair factors of 210 are (1, 210), (2, 105), (3, 70), ( 5, 42), (6, 35), (7, 30), (10, 21), and (14, 15).
What are all the positive pair factors of 210?
The positive pair factors of 210 are (1,210), (2,105), (3,70), (5,42), (6,35), (7,30), (10,21), and (14,15).
How many factors of 210 are perfect squares?
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
No factor of 210 is a perfect square.
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