What is meant by the Term ‘Factors of 96’?
Numbers which are a factor of 96 can evenly divide 96 leaving no remainder. If 2 is to be a factor of 96, for example, 96 must be evenly divisible by 2, that is, the remainder after division is zero.
As a result, 2 is one of the factors of 96. The quotient obtained on division of a number by its factor is also a factor of the original number. So here 48 is also a factor of 96.
Because 96 is a composite number it will have more than just the two usual factors of 1 and the number itself, which is 96. Let’s look at how to find the other factors of 96 and along with that, we’ll also study the factor pairs and prime factorization of 96.
Determining the Factor List of 96
To determine the factors of 96, we must first determine which natural number divides 96 evenly and leaves no remainder. Divisibility rules and division facts can be used to determine the factors of 96.
We can stop checking after 10 as the factor pairs start to repeat.
So the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Prime Factors of 96
The term “prime factorization” refers to the representation of a number as a product of prime numbers. Here the prime numbers multiplied are known as the prime factors of the original number.
Prime Factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3 = 2\(^5\) x 3
So the prime factors of 96 are 2 and 3.
Factor Pairs of 96
A factor pair of a number is the set of two of its factors, such that their product is the number itself.
So the factor pair of 96 is a set of two of its factors such that their product is 96.
For example (1, 96) is a factor pair of 96 as 1 x 96 = 96.
Factors pairs of a number can be written from the list of its factors. A factor pair can be a positive pair or a negative pair.
Here is a list of positive factor pairs of 96
Hence, the factor pairs of 96 are (1, 96), (2, 48), (3, 32), (4, 24), (6, 16) and (8, 12).
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Rapid Recall
Factors of 96
Solved Factors of 96 Examples
Example 1: What are the common factors of the numbers 96 and 69?
Solution:
The factors of 96 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
The factors of 69 are:
1, 3, 23 and 69
So the common factors of 96 and 69 are 1 and 3
Example 2: What is the sum of the factors of 96?
Solution:
The factors of 96 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
Sum of the factors = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96
Sum = 252
So the sum of all factors of 96 is 252.
Example 3: What is the greatest common factor of 96 and 84?
Solution:
The factors for the number 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
The factors of the number 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.
The common factors of 96 and 84 are 1, 2, 3, 4, 6, and 12.
So the greatest common factor of both these numbers is 12.
Example 4: A team of four cooks was asked to make 96 pies. Later on, two other teams of cooks, one with 6 cooks and the other with 8, were also asked to make 96 pies per team. How many pies does each cook make from the three different teams?
Solution:
There are a total of three teams with 4, 6 and 8 cooks respectively. Each team prepares 96 pies. To figure out the number of pies each cook has to prepare, we will list the factor pairs of 96.
(1, 96)
(2, 48)
(3, 32)
(4, 24)
(6, 16)
(8, 12)
We do not need the first three pairs. We will take the last three pairs into consideration.
4 x 24 = 96
6 x 16 = 96
8 x 12 = 96
So if there are 4 cooks, each cook has to make 24 pies. If there are 6 cooks, each cook has to make 16 pies and if there are 8 cooks, each cook has to make 12 pies.
[Note: Here we have assumed that in a team all cooks prepare an equal number of pies.]
Factors of a number are natural numbers that divide it evenly leaving no remainder.
96 has more than two factors. This means that 96 is not a prime number.
For any number to be divisible by 5, its units’ place digit should be either 0 or 5. 96 has neither of these digits, hence it is not evenly divisible by 5. So 5 is not a factor of 96.
A number that has more than two factors is a composite number. 96 has 12 factors, hence it is a composite number.