The factors of 156 are the numbers that divide 156 exactly without leaving any remainder value. The factors and the pair factors of 156 can be expressed in positive and negative form. For example, the pair factor of 156 is represented by (1, 156) or (-1, -156). If we multiply a pair of negative numbers, such as multiplying -1 and -156, it will result in the original number 156.
In this article, we will learn the factors of 156, positive and negative pair factors of 156, how to find the prime factors of 156 using the prime factorization method, and many solved examples.
Table of Contents:
- What are the Factors of 156?
- Pair Factors of 156
- Factors of 156 by Division Method
- Prime Factorization of 156
- Solved Examples
- FAQs
What are the Factors of 156?
The numbers that divide 156 completely without leaving a remainder value are the factors of 156. In other words, the numbers multiplied in pairs resulting in the original number 156 are the factors of 156. As 156 is a composite number, it has many factors other than 1 and 156. Thus, the factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156. Similarly, the negative factors of 156 are -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78 and -156.
Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156. Prime Factorization of 156: 2 × 2 × 3 × 13 or 2^{2} × 3 × 13. |
Pair Factors of 156
A pair of numbers that are multiplied together resulting in the number 156 is called the pair factor of 156. As 156 is a composite number, it has more than one pair factor. The following are the positive and negative pair factors of 156.
Positive Pair Factors of 156:
Positive Factors of 156 |
Positive Pair Factors of 156 |
1 × 156 |
(1, 156) |
2 × 78 |
(2, 78) |
3 × 52 |
(3, 52) |
4 × 39 |
(4, 39) |
6 × 26 |
(6, 26) |
12 × 13 |
(12, 13) |
Therefore, the positive pair factors of 156 are (1, 156), (2, 78), (3, 52), (4, 39), (6, 26) and (12, 13).
Negative Pair Factors of 156:
Negative Factors of 156 |
Negative Pair Factors of 156 |
-1 × -156 |
(-1, -156) |
-2 × -78 |
(-2, -78) |
-3 × -52 |
(-3, -52) |
-4 × -39 |
(-4, -39) |
-6 × -26 |
(-6, -26) |
-12 × -13 |
(-12, -13) |
Hence, the negative pair factors of 156 are (-1, -156), (-2, -78), (-3, -52), (-4, -39), (-6, -26) and (-12, -13).
Factors of 156 by Division Method
In the division method, the factors of 156 are found by dividing the number 156 by various integer numbers. If the integers divide 156 evenly without leaving a remainder, then those integers are the factors of 156. The factors of 156 using the division method are found as follows:
- 156/1= 156 (Factor = 1 and Remainder = 0)
- 156/2 = 78 (Factor = 2 and Remainder = 0)
- 156/3 = 52 (Factor = 3 and Remainder = 0)
- 156/4 = 39 (Factor = 4 and Remainder = 0)
- 156/6 = 26 (Factor = 6 and Remainder = 0)
- 156/12 = 13 (Factor = 12 and Remainder = 0)
- 156/13 = 12 (Factor = 13 and Remainder = 0)
- 156/26 = 6 (Factor = 26 and Remainder = 0)
- 156/39 = 4 (Factor = 39 and Remainder = 0)
- 156/52 = 3 (Factor = 52 and Remainder = 0)
- 156/78 = 2 (Factor = 78 and Remainder = 0)
- 156/156 = 1 (Factor = 156 and Remainder = 0)
If we divide 156 by any numbers other than 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156, it leaves a remainder value. Hence, the factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
Prime Factorization of 156
The process of writing 156 as the product of its prime factors is called the prime factorization of 156. Go through the following procedure to find the prime factors of 156.
Take the pair factor of 156, say (1, 156)
Here, the number 156 is an even composite number, which can be further divided into its prime factors. Thus, 156 is written as the product of 12 and 13.
Here, 13 is a prime number, and 12 is a composite number that can again split as 4×3 and which is equal to 2 × 2 × 3.
Now, write all the obtained numbers in the product form.
Thus, 156 is written as 2 × 2 × 3 × 13.
Therefore, the prime factorization of 156 is 2 × 2 × 3 × 13 or 2^{2} × 3 × 13, where 2, 3 and 13 are prime numbers.
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Solved Examples
Example 1:
Find the common factors of 156 and 157.
Solution:
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
The factors of 157 are 1 and 157.
As the number 157 is a prime number, the common factor of 156 and 157 is 1.
Example 2:
What are the common factors of 156 and 155?
Solution:
Factors of 156 = 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
Factors of 155 = 1, 5, 31 and 155.
Thus, the common factor of 156 and 155 is 1.
Example 3:
Find the common factors 156 and 39.
Solution:
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
The factors of 39 are 1, 3, 13 and 39.
Therefore, the common factors of 156 and 39 are 1, 3, 13 and 39.
Frequently Asked Questions 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 is the prime factorization of 156?
The prime factorization of 156 is 2 × 2 × 3 × 13 or 2^{2} × 3 × 13.
Write down the positive pair factors of 156.
The positive pair factors of 156 are (1, 156), (2, 78), (3, 52), (4, 39), (6, 26) and (12, 13).
What are the negative pair factors of 156?
The negative pair factors of 156 are (-1, -156), (-2, -78), (-3, -52), (-4, -39), (-6, -26) and (-12, -13).
Is 52 a factor of 156?
Yes, 52 is a factor of 156. As 52 divides 156 exactly and leaves a quotient value of 3 and remainder value as 0, and hence, 52 is a factor of 156.