Factors of 88 Using Prime Factorization
Factors of 88
What are the Factors of 88?
Numbers that divide 88 without leaving any remainder are known as the factors of 88.
For Example:
2 is a factor of 88 because when we divide 88 by 2 it results in the quotient as 44 and the remainder as 0. The quotient is also a factor of 88.
Thus, to check if a number is a factor of 88 or not, divide 88 by that number, and if the remainder is zero, then, that number is said to be a factor of 88.
Factor List of 88
The divisibility rules and division facts can be used to find the factors of 88.
Therefore the factors of 88 are 1, 2, 4, 8, 11, 22, 44, and 88.
Prime Factors of 88
The number 88 is a composite number, that is, it has more than two numbers as factors. To carry out prime factorization of 88, we will keep dividing 88 by its prime factors, until we get the result as 1.
As 88 is even, let’s start dividing by 2.
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
Now 11 is a prime number itself, so we will divide by 11;
11 ÷ 11 = 1
So, the prime factorization of 88 = 2 × 2 × 2 × 11 or \(2^3\) × 11.
This shows us that 2 and 11 are the only prime factors of 88.
Factor Pairs of 88
Factor pairs of 88 is a set of two factors of 88 that when multiplied together give the product as 88. We also need to note that factors can exist as positive or negative pairs.
We can write the positive factor pairs of 88 from the list of its factors.
Hence, the positive factor pairs of 88 are (1, 88), (2, 44), (2, 22) and (8, 11).
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Rapid Recall
Factors of 88 are;
Solved Factors of 88Examples
Example 1: Find the factors common between 88 and 90.
Solution:
Factors of 88 = 1, 2, 4, 8, 11, 22, 44, and 88
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Therefore, the factors common between 88 and 90 are 1 and 2.
Example 2: Find the factors common between 83 and 88.
Solution:
Factors of 83 = 1 and 83
Factors of 88 = 1, 2, 4, 8, 11, 22, 44, and 88
Therefore, the factor common between 83 and 88 is 1.
Example 3: Patrick has to travel 88 miles at an average speed of 22 mph. In how many hours will he cover the total distance?
Solution:
Total distance to be covered = 88 miles
Speed = 22 mph
To find the total number of hours to reach the destination, we will have to divide the total distance by the speed, that is,
\(\frac{88}{22}\)
= \(\frac{22~\times~4}{22}\) [(22,4) is a factor pair of 88]
= 4 [Divide both the numerator and the denominator by 22]
Therefore Patrick will take 4 hours to cover the total distance.
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, and 88.
So, the least factor of 88 is 1 and the greatest factor is 88 itself.
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, and 88.
Sum of factors = 1 + 2 + 4 + 8 + 11 + 22 + 44 + 88 = 180
So, the sum of factors of 88 is 180.
Yes, 22 is a factor of 88 as 22 divides 88 exactly without leaving any remainder.
A factor of 88 is a natural number which evenly divides 88, leaving a zero remainder. Whereas a multiple of 88 is a number obtained by multiplying a natural number by 88. So a factor of 88 is associated with division of 88 and a multiple of 88 is associated with multiplication by 88.
When two negative numbers are multiplied together the resulting product is positive. The negative factor pairs are pairs of numbers whose product is the same as positive factor pairs.
The negative factor pairs of 88 are: (-1, -88), (-2, -44), (-2, -22) and (-8, -11) .