Did you know that 55 is the sum of the first 10 natural numbers i.e. 1+2+3+4+5+6+7+8+9+10=55 and it is also the sum of the squares of the first 5 natural numbers i.e. 1+4+9+16+25=55? In this lesson, we will calculate the factors of 55, the prime factors of 55, and the factors of 55 in pairs. We will also go through a few solved examples.
The numbers by which 55 is divisible are the factors of 55. For example, 55 is divisible by 11. Hence, 11 is a factor of 55.
Can you think of other factors of 55?
Tips and Tricks:
When you divide a number by its factor, the quotient of the division is also a factor.
An odd number cannot have even factors.
Divisibility rules make the process of finding factors easy.
How to Calculate the Factors of 55?
We have learnt that the factors of 55 can be found using division. We can find the factors of 55 using multiplication as well. Can you think of two numbers whose product is 55? Can you think of all such possibilities?
The multiplicands of each such product are the factors of 55.
Hence, the factors of 55 are 1, 5, 11 and 55.
Explore factors using illustrations and interactive examples
The prime factorization of 55 is expressing 55 as the product of prime numbers which gives the result as 55. Thus, the prime factorization of 55 is 55 = 5 × 11. From the prime factorization of 55, it is clear that 5 and 11 are the prime factors of 55. We know that 1 is the factor of every number.
Thus, the factors of 55 by prime factorization are 1, 5, 11, and 55.
Can you find the common factors of 55, 60 and 65?
Factors of 55 in Pairs
The pair factors of 55 are obtained by writing 55 as a product of two numbers in all possible ways. In each product, both multiplicands form the pair factors of 55.
The factors of 55 are 1, 5, 11, and 55.
Product that Results in 55
Pair Factors of 55
1 × 55
5 × 11
The negative pair factors of 55 are (-1, -55) and (-5, -11).
Factors of 55 Solved Examples
Example 1: Isabella, a dance teacher, wants to arrange 55 students of her dance class into groups for dance practice. She wants each group to have equal number of students. She also doesn't want to form a group for either one student or all students. Based on this information, what can be the possible size(s) of the group?
We already learned that the factors of 55 are 1, 5, 11, and 55. Since a group cannot have 1 or all the students, each group can have either 5 or 11 students.
Hence, the size of each group = 5 (or) 11.
Example 2: William is stuck with finding the common factors of 55 and 60. Can we help him?
We have already learned that, the factors of 55 are 1, 5, 11 and 55. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Hence, the factors that are common to both 55 and 60 are 1 and 5.