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Factors of 156
Did you know that 156 is an even composite number whose product constitues three primes, namely 2, 3, and 13? Hence, 3 pair factors of 156 will contain each prime number. In this chapter, we will calculate the factors of 156, prime factors of 156, and factors of 156 in pairs along with solved examples and interactive questions for a better understanding.
 Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156
 Prime Factorization of 156: 156 = 2^{2} × 3 × 13
What Are the Factors of 156?
Factors of 156 are the numbers which on multiplication give 156. The numbers which divide 156 without leaving any remainder are the factors of 156. So, when we multiply any two whole numbers with each other and obtain 156 as the answer, both the numbers are said to be the factors of 156.
How to Calculate the Factors of 156?
We can calculate the factors of 156 by finding all the numbers which divide 156 without leaving any remainder. Let's start by checking for the factors of 156, starting from 1 to 156. It is possible to express 156 as a product of its prime factors in the prime factorization method. We divide 156 with its divisors in the division method. For the numbers which divide 156 entirely, the divisors as well as their quotients are the factors of 156.
Numbers Dividing 156  Factors of 156 

156/1 = 156  1 and 156 are factors of 156. 
156/2 = 78  2 and 78 are factors of 156. 
156/3 = 52  3 and 52 are factors of 156. 
156/4 = 39  4 and 39 are factors of 156. 
156/6 = 26  6 and 26 are factors of 156. 
156/12 = 13  12 and 13 are factors of 156. 
Hence, the factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.
Explore factors using illustrations and interactive examples.
 Factors of 169  The factors of 169 are 1, 13, and 169,
 Factors of 105  The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.
 Factors of 150  The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
 Factors of 132  The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.
 Factors of 12  The factors of 12 are 1, 2, 3, 4, 6, and 12.
 Factors of 13  The factors of 13 are 1 and 13.
Factors of 156 by Prime Factorization
When we express a composite number as the product of its prime factors, it is called prime factorization. To get the prime factorization of 156, we use two methods:
 Method 1: Factor Tree Method
 Method 2: UpsideDown Division Method
Method 1: Factor Tree Method
The factor tree of 156 is:
Method 2: UpsideDown Division Method
On dividing 156 by its smallest prime factor which is 2, we get
156/2 = 78
Now, 78 is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1.
The prime factorization of 156 is shown below:
Hence, the prime factors of 156 are 2, 3, and 13.
The prime factorization of 156 is 2 × 2 × 3 × 13.
Factors of 156 in Pairs
Numbers, which on multiplication give 156, are known as the factor pairs of 156. Observe the following factors of 156 in pairs. We can also obtain negative pair factors as the product of two negative numbers is a positive number (  ve ×  ve ) = +ve.
 Positive Pair Factors of 156 are: (1, 156), (2, 78), (3, 52), (4, 39), (6, 26), (12, 13)
 Negative Pair Factors of 156 are: (1, 156), (2, 78), (3, 52), (4, 39), (6, 26), (12, 13)
Important Notes:
 As 156 ends with 56 as the last two digits and 56 is divisible by 4, 4 is one of the factors of 156.
 As the sum of the digits of 156 is 12 (divisible by 3), 3 is one of the factors of 156.
 156 is a nonperfect square number. Hence, it has an even number of factors.
Challenging Questions:
 Are 0.156 and 5/4 factors of 156? Why do you think so?
Factors of 156 Solved Examples

Example 1: Can you find the common factors of 156 and 165?
Solution:
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, and 165.Hence, the common factors of 156 and 165 are 1 and 3.

Example 2: Andy has a 156 square inches rectangular box. If the length of the box is 13 inches, can you help him find the breadth of the box?
Solution:
The area of the given rectangular box is 156 square inches with length of the box being 13 inches.
To determine the area of the rectangle, we use the formula: area = length × breadth.The breadth of the box will be given by the formula: breadth = area/length = 156/13 = 12.
Hence, the breadth of the rectangular box is 12 inches.
FAQs on Factors of 156
What are the factors of 156?
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.
What are the prime factors of 156?
The prime factors of 156 are 2, 3, and 13.
Are all the factors of 156 prime?
No, all the factors of 156 are not prime.
What are the common factors of 156 and 108?
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Hence, the common factors of 156 and 108 are 1, 2, 3, 4, 6, and 12.
Is 9 a factor of 156?
No, 9 is not a factor of 156.
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