What are the factors of 55?
Natural numbers that can divide a number evenly without leaving a remainder are known as the factors of that particular number. When 55 is divided by its factor, the remainder is zero and the quotient is also a factor of 55.
The number 55 has a total of four factors: 1, 5, 11 and 55.
List of factors of the number 55
The factors of 55 can be obtained using divisibility rules and division facts.
So the factor list of 55 is : 1, 5, 11 and 55.
[Note: To determine whether a number is a factor of 55 or not, divide 55 by that number and check whether the remainder is zero or not. If the remainder is zero then the number is a factor of 55.]
Prime factors of 55
The factor tree below depicts the prime factorization of the number 55.
So the prime factorization of 55 is given by 5 x 11 and the prime factors of 55 are 5 and 11.
Factor pairs of 55
A factor pair of 55 is a set of two factors of 55 such that their product is 55. A number can have a positive pair of factors and a negative pair of factors.
For example, (1, 55) is a factor pair of 55.
1 x 55 = 55
Below is a list of positive factor pairs of 55.
So, the factor pairs for 55 are (1, 55) and (5, 11).
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Solved Factors of 55 Examples
Example 1: Find the sum of all factors of 55 and find the average.
Solution: The factors of 55 : 1, 5, 11, 55
Sum of all factors = 1 + 5 + 11 + 55 = 72
Total number of factors of 55 = 4
Average of factors of 55 = \(\frac{72}{4}\) = 18
Hence, the sum and average of the factors of 55 is 72 and 18 respectively.
Example 2 : Find the greatest common factor of 55 and 110.
Solution: To find the greatest common factor of 55 and 110, list the factors of 55 and 110 and select the highest common factor.
Factors of 55 : 1, 5, 11, 55
Factors of 110 : 1, 2, 5, 10, 11, 22, 55, 110
The common factors of 55 and 110 : 1, 5, 11, and 55
The greatest of these factors is 55.
Therefore, the greatest common factor of 55 and 110 is 55.
Example 3: A contractor buys 55 solar panels . He wants to organize the panels into a rectangular array. How many different arrays can he make?
Solution: To find the number of array the contractor can make , Find the number of factor pairs of 55
Factors of 55 : 1, 5, 11, 55
So, there are two factor pairs for 55 : (1, 55) and (5, 11).
You can use each factor pair to make 2 arrays.
Since there are 2 factor pairs so 2 x 2 = 4 ways to organize the panels in different arrays.
Factors of any number will be divisors which exactly divide the number that leaves zero as the remainder.
The prime factor of a number is that factor of the number which is a prime number.
To identify whether a number is prime or not we need to find out the factors of the number. If the number does not have factors other than 1 and the number itself, it will be a prime number.
Factors of 55 : 1, 5, 11, 55
Since 55 has factors other than 1 and itself (55) so 55 is not a prime number.
Two prime numbers are said to be twin prime or prime pairs if they have a difference of 2 between them.
Ex- (3 and 5), (5 and 7), (11, 13), (17, 19) etc
Twin prime numbers between 1 to 50 are :
(3 and 5), (5 and 7), (11 and 13), (17 and 19), (29 and 31), (41 and 43)