The factors of 182 are the numbers that divide 182 evenly without leaving a remainder value. The factors and the pair factors of 182 can be represented in both positive and negative form. For example, the factors of 182 can be represented as (1, 182) or (-1, -182). We know that the multiplication of two negative numbers results in a positive number. Hence, if we multiply -1 and -182, it will result in the original number 182.
In this article, we are going to learn the factors of 182, the positive and negative factors of 182, how to find the prime factors of 182 using the prime factorization method and many solved examples.
Table of Contents:
- What are the Factors of 182?
- Pair Factors of 182
- Factors of 182 by Division Method
- Prime Factorization of 182
- Solved Examples
- FAQs
What are the Factors of 182?
The numbers that divide 182 completely and leave a remainder 0 are the factors of 182. In other words, the numbers that are multiplied together in pairs resulting in the number 182 are the factors of 182. As the number 182 is an even composite number, it has many factors other than 1 and 182. Therefore, the factors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Similarly, the negative factors of 182 are -1, -2, -7, -13, -14, -26, -91 and -182.
Factors of 182: 1, 2, 7, 13, 14, 26, 91 and 182. Prime Factorization of 182: 2 × 7 × 13. |
Pair Factors of 182
The pair factors of 182 are the pair of numbers, in which the two numbers in the pair are multiplied together resulting in the original number 182. Since 182 is a composite number, it has more than one pair factor. Thus, the positive and negative pair factors of 182 are given below:
Positive Pair Factors of 182:
Positive Factors of 182 |
Positive Pair Factors of 182 |
1 × 182 |
(1, 182) |
2 × 91 |
(2, 91) |
7 × 26 |
(7, 26) |
13 × 14 |
(13, 14) |
Therefore, the positive pair factors of 182 are (1, 182), (2, 91), (7, 26) and (13, 14).
Negative Pair Factors of 182:
Negative Factors of 182 |
Negative Pair Factors of 182 |
-1 × -182 |
(-1, -182) |
-2 × -91 |
(-2, -91) |
-7 × -26 |
(-7, -26) |
-13 × -14 |
(-13, -14) |
Hence, the negative pair factors of 182 are (-1, -182), (-2, -91), (-7, -26) and (-13, -14)
Factors of 182 by Division Method
In the division method, the factors of 182 are found by dividing the number 182 by different integer numbers. If the integer divides 182 completely without leaving any remainder, then the integer is a factor of 182. Now, let us start dividing 182 by 1 and then proceed with the different numbers.
- 182/1 = 182 (Factor is 1 and Remainder is 0)
- 182/2 = 91 (Factor is 2 and Remainder is 0)
- 182/7 = 26 (Factor is 7 and Remainder is 0)
- 182/13 = 14 (Factor is 13 and Remainder is 0)
- 182/14 = 13 (Factor is 14 and Remainder is 0)
- 182/26 = 7 (Factor is 26 and Remainder is 0)
- 182/91 = 2 (Factor is 91 and Remainder is 0)
- 182/182 =1 (Factor is 182 and Remainder is 0)
If we divide 182 by any numbers other than 1, 2, 7, 13, 14, 26, 91 and 182, it leaves a remainder value. Hence, the factors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Prime Factorization of 182
The prime factorization of 182 is the method of writing the number 182 in the form of a product of its prime factors. Since 182 is composite, it can be further factored into its prime factors. Go through the following procedure to find the prime factors of 182 using the prime factorization method.
Consider a pair factor of 182, say (1, 182)
Now, write the number 182 in terms of its prime factors. Thus, 182 is written as the product of 13 and 14. Here, 13 is a prime number and 14 is a composite number, which can again split as the product of 2 and 7.
Thus, 182 is written as 2 × 7 × 13.
Therefore, the prime factorization of 182 is 2 × 7 × 13 or 2^{1} × 7^{1} × 13^{1}, where 2, 7 and 13 are prime numbers.
We can easily find the number of factors of 182 with the help of the prime factorization method. As discussed above, the prime factorization of 182 is 2^{1} × 7^{1} × 13^{1}. The exponent values in the prime factorization of 182 are 1, 1 and 1. Now, add the number 1 to the exponent values and then multiply with the obtained values.
(i.e.) (1+1)×(1+1)×(1+1) = 2×2×2 = 8
Hence, the number 182 has 8 factors.
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Solved Examples
Example 1:
Find the common factors of 182 and 181.
Solution:
The factors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
The factors of 181 are 1 and 181.
Thus, the common factor of 182 and 181 is 1, as the number 181 is a prime number.
Example 2:
Find the common factors of 182 and 183.
Solution:
Factors of 182 = 1, 2, 7, 13, 14, 26, 91 and 182.
Factors of 183 = 1, 3, 61 and 183.
Thus, the common factor of 182 and 183 is 1.
Example 3:
What are the common factors of 182 and 91?
Solution:
The factors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
The factors of 91 are 1, 7, 13 and 91.
Therefore, the common factors of 182 and 91 are 1, 7, 13 and 91.
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Frequently Asked Questions on Factors of 182
What are the factors of 182?
The factors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
What is the prime factorization of 182?
The prime factorization of 182 is 2 × 7 × 13.
What are the positive pair factors of 182?
The positive pair factors of 182 are (1, 182), (2, 91), (7, 26) and (13, 14).
What are the negative pair factors of 182?
The negative pair factors of 182 are (-1, -182), (-2, -91), (-7, -26) and (-13, -14)
Is 14 a factor of 182?
Yes, 14 is a factor of 182. As 14 divides 182 exactly and leaves a remainder 0, 14 is a factor of 182.