Factors of 182 Using Prime Factorization
What are Factors?
The numbers that are multiplied together in pairs, resulting in the number 182, are the factors of 182. In other words, the number that divides 182 completely without leaving a remainder is known as the factor of 182. If we get a non-zero remainder when 182 is divided by a number, that number will not be a factor of 182. The factors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. No other positive integer can divide 182 completely.
Divisibility Rule to Find the Factors of 182
Factors of 182 by Division Method
If we divide 182 by 1, we get 182 and 0 as the quotient and the remainder, respectively. So, 1 is the factor of 182.
If we divide 182 by 2, we get 91 and 0 as the quotient and the remainder, respectively. So, 2 is the factor of 182.
If we divide 182 by 7, we get 26 and 0 as the quotient and the remainder, respectively. So, 7 is the factor of 182.
If we divide 182 by 13, we get 14 and 0 as the quotient and the remainder, respectively. So, 13 is the factor of 182.
If we divide 182 by 14, we get 13 and 0 as the quotient and the remainder, respectively. So, 14 is the factor of 182.
If we divide 182 by 26, we get 7 and 0 as the quotient and the remainder, respectively. So, 26 is the factor of 182.
If we divide 182 by 91, we get 2 and 0 as the quotient and the remainder, respectively. So, 91 is the factor of 182.
If we divide 182 by 182, we get 1 and 0 as the quotient and the remainder, respectively. So, 182 is the factor of 182.
Prime Factorization of 182
A natural number can be obtained by multiplying some prime numbers. Then, the prime numbers are known as the prime factors of that natural number. The process of writing this multiplication of prime factors is known as prime factorization.
Since 182 is a composite number having composite factors, we can divide those composite factors to get prime factors. We can divide 182 by a natural number less than itself to obtain the prime factorization. The prime factorization of 182 can be represented using a factor tree as follows:
So, the prime factorization of 182 is 182 = 2 \(\times\) 7 \(\times\) 13.
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Factor Pairs of 182
The factor pairs of 182 are the pairs of numbers whose multiplication is 182. The factors of 182 are :
1 \(\times\) 182 = 182 ⇒ (1, 182)
2 \(\times\) 91 = 182 ⇒ (2, 91)
7 \(\times\) 26 = 182 ⇒ (7, 26)
13 \(\times\) 14 = 182 ⇒ (13, 14)
We can also write the factor pairs in ordered pairs: (1, 182), (2, 91), (7, 26) and (13, 14).
Rapid Recall
Solved Factors of 182 Examples
Example 1: Find the common factors of 84 and 182.
Solution:
The factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
The factors of 182 = 1, 2, 7, 13, 14, 26, 91 and 182
Therefore, the common factors of 84 and 182 are 1 and 7.
Example 2: Find the greatest common factor of 120 and 182.
Solution:
The factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
The factors of 182 = 1, 2, 7, 13, 14, 26, 91 and 182
The common factors of 120 and 182 are 1 and 2.
Therefore, the greatest common factor of 120 and 182 is 2.
Example 3: Ryan wants to know the age of his eldest cousin, Thomas. Thomas asks Ryan to solve a riddle to know his age. Thomas says, “I am as old as the sum of all the prime factors of 182”. How old is Thomas?
Solution:
The prime factors of 182 are 2, 7 and 13.
The sum of the prime factors = 2 + 7 + 13
= 22
The sum of all the prime factors of 182 is 22.
Therefore, Thomas is 22 years old.
Example 4: Can 182 be completely divided by 5?
Solution:
No, the ones digit is neither 0 nor 5.
So, when we divide 182 by 5, we get 36 and 2 as the quotient and the remainder, respectively.
The factor pairs of 182 are (1, 182), (2, 91), (7, 26) and (13, 14).
The prime factors of 182 are 2, 7 and 13.
The product of the prime factors = 2 \(\times\) 7 \(\times\) 13 = 182.
Composite numbers are those numbers which have a factor other than 1 or itself. For example 14, 15, 16 and so on.
The factors of 182 are 1, 2, 7, 13, 14, 26 and 182.
So, the smallest factor of 182 is 1, and the greatest factor is 182 itself.