Factors
Factors of 96 | Prime Factorization of 96 | Factor Tree of 96
Written by Prerit Jain
Updated on: 24 Aug 2023
Contents
Factors of 96 | Prime Factorization of 96 | Factor Tree of 96
Factors of 96
| Factors of 96 | Factor Pairs of 96 | Prime factors of 96 |
| 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. | (1,96) (2,48) (3,32) (4,24) (6,16) (8,12) (12,8) (16,6) (24,4) (32,3) (48,2) | 2 × 2 × 2 × 2 × 2 × 3 |
Calculate Factors of
The Factors are
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What are the factors of 96
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. These are all of the integers that can be evenly divided by 96.
To find the factors of 96, we can divide 96 by each number between 1 and 96 to see if there is no remainder. If there is no remainder, then the number is a factor of 96.
For example, when we divide 96 by 1, there is no remainder, so 1 is a factor of 96. When we divide 96 by 2, there is no remainder, so 2 is a factor of 96. When we divide 96 by 3, there is a remainder of 0, so 3 is a factor of 96. And so on.
How to Find Factors of 96
The following are the methods through which you can find the factors of 96:
- Factors of 96 using the Multiplication Method
- Factors of 96 using the Division Method
- Prime Factorization of 96
- Factor tree of 96
Factors of 96 Using the Multiplication Method
The multiplication method is a way to find the factors of a number by listing out the pairs of numbers that multiply to give us the target number.
For example, let’s find the factors of 97 using the multiplication method. We can start by listing out the pairs of numbers that multiply to give us 97:
1 x 97 = 97
We can see that the pair of numbers that multiplies to give us 97 is (1, 97). These are the factors of 97.
This method can be a helpful way to find the factors of a number, especially if the number is large and it would be time-consuming to divide it by all of the numbers between 1 and itself to find the factors.
Factors of 96 Using the Division Method
The division method is a way to find the factors of a number by dividing the number by each number between 1 and itself to see if there is no remainder. If there is no remainder, then the number is a factor of the target number.
For example, let’s find the factors of 96 using the division method. We can start by dividing 96 by 1:
96 ÷ 1 = 96 (There is no remainder, so 1 is a factor of 96)
Then we can divide 96 by 2:
96 ÷ 2 = 48 (There is no remainder, so 2 is a factor of 96)
Then we can divide 96 by 3:
96 ÷ 3 = 32 (There is no remainder, so 3 is a factor of 96)
We can keep going like this until we reach 96, and we will find that the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
This method can be a helpful way to find the factors of a number, especially if the number is small and it would be quick to divide it by all of the numbers between 1 and itself.
Prime Factorization of 96
Calculate Prime Factors of
The Prime Factors of 96 =
2 x
2 x
2 x
2 x
2 x
3
In prime factorization, we try to break a number down into its prime factors, which are numbers that can only be divided by 1 and themselves. For example, the prime factors of 6 are 2 and 3, because 2 x 3 = 6, and 2 and 3 can only be divided by 1 and themselves.
To find the prime factorization of 96, we can start by dividing 96 by the smallest prime number, which is 2. When we divide 96 by 2, we get 48, which is a whole number. This means that 2 is a factor of 96.
Continue dividing the quotient by 2 until it is no longer divisible evenly. The next quotient is 24, then 12, 6 and finally 3.
So, the prime factorization of 96 is 3 x 2^5. In other words, 96 can be expressed as the product of the prime factors 3 and 2^5.
Factor tree of 96
- Start with 96 at the top of the tree.
- Divide 96 by the smallest prime factor, which is 2. The result is 48.
- Write 2 and 48 as the two branches of the tree.
- Continue dividing 48 by 2. The result is 24.
- Write 2 and 24 as the next branches of the tree.
- Divide 24 by 2 again. The result is 12.
- Write 2 and 12 as the next branches of the tree.
- Divide 12 by 2 once more. The result is 6.
- Write 2 and 6 as the next branches of the tree.
- Since 6 is divisible by 2, divide it again. The result is 3.
- Write 2 and 3 as the final branches of the tree.
- Since 3 is a prime number, write it at the end of the branches.
Here is what the factor tree for 96 looks like:
96
|
3
|
32
The prime factorization of 96 is the product of the numbers at the bottom of the factor tree. In this case, the prime factorization of 96 is 3 x 32.
Factor Pairs of 96
Calculate Pair Factors of
1 x 96=96
2 x 48=96
3 x 32=96
4 x 24=96
6 x 16=96
8 x 12=96
12 x 8=96
16 x 6=96
24 x 4=96
32 x 3=96
48 x 2=96
So Pair Factors of 96 are
(1,96)
(2,48)
(3,32)
(4,24)
(6,16)
(8,12)
(12,8)
(16,6)
(24,4)
(32,3)
(48,2)
Factor pairs are pairs of numbers that, when multiplied together, give us the target number. To find the factor pairs of a number, we can divide the number by each number between 1 and itself to see if there is no remainder. If there is no remainder, then the number and the result of the division are a pair of factors.
For example, let’s find the factor pairs of 96. We can start by dividing 96 by 1:
96 ÷ 1 = 96 (There is no remainder, so 1 and 96 are a pair of factors)
Then we can divide 96 by 2:
96 ÷ 2 = 48 (There is no remainder, so 2 and 48 are a pair of factors)
Then we can divide 96 by 3:
96 ÷ 3 = 32 (There is no remainder, so 3 and 32 are a pair of factors)
We can keep going like this until we reach 96, and we will find that the factor pairs of 96 are (1, 96), (2, 48), (3, 32), (4, 24), (6, 16), and (8, 12).
More Factors
- Factors of 93
- Factors of 94
- Factors of 95
- Factors of 96
- Factors of 97
- Factors of 98
- Factors of 99
Factors of 96 – Quick Recap
- Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
- Negative Factors of 96: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -96.
- Prime Factors of 96: 2 × 2 × 2 × 2 × 2 × 3
- Prime Factorization of 96: 2 × 2 × 2 × 2 × 2 × 3
Factors of 96 – Fun Facts
- 96 is an even number, so it has an even number of factors. In this case, 96 has 12 factors.
- 96 is not a prime number, because it has more than 2 factors. Prime numbers are only divisible by 1 and themselves.
- 96 is a composite number because it has more than 2 factors. Composite numbers are numbers that are not prime and are made up of the product of two or more prime numbers. In the case of 96, the prime factorization is 2^5 x 3.
- The factors of 96 are all integers. This means that they are all whole numbers, and they are not fractions or decimals.
- The factors of 96 include both positive and negative integers. This means that 96 can be evenly divided by both positive and negative numbers.
Also Check: Multiples, Square Root, and LCM
Solved Examples of Factor of 96
Q.1: Tom has 96 marbles and wants to divide them into 7 equal piles. How many marbles will be in each pile?
Solution: Divide the total number of marbles (96) by the number of piles (7): 96 ÷ 7 = 13 remainders 5. Therefore, each pile will have 13 marbles, and there will be an additional 5 marbles remaining.
Q.2:Sally was given 96 balloons for her birthday party, but can only hang 19 balloons in the room at once, how many times will she need to fill the room with balloons?
Solution: Divide 96 by 19: 96 ÷ 19 = 5 remainders 1. Therefore, Sally will need to fill the room with balloons 5 times, and there will be 1 balloon remaining that cannot fill the room.
Q.3 Bill has an aquarium of size 96 litres and wants to add eight fish that take up 11 litres each, can he fit all the fish in the aquarium?
Solution: Yes, 8 fish will take up 88 litres of space which is less than the size of the aquarium.
Q.4: Jack is baking 96 cookies and wants to divide them equally into 5 plates. How many cookies will be on each plate?
Solution: 96 cookies ÷ 5 plates = 19 cookies per plate (with a remainder of 1 cookie). Therefore, each plate will have 19 cookies, and there will be 1 cookie left over.
Q.5: Mary had 96 coins and gave 4 coins to her cousin. How many coins does she have left?
Solution: 92 coins left.
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Frequently Asked Questions on Factors of 96
Juan is trying to find the greatest common factor of 96 and 216. What is it?
The greatest common factor of 96 and 216 is 24 because both numbers are divisible by 24.
What number when multiplied by 6 will yield 96?
16 is the number that when multiplied by 6 will yield 96 (6 x 16 = 96).
Richard needs to find the least common multiple for 24, 32, and 48. What is it?
Let’s first find the prime factorization of each number: 24 = 2^3 * 3^1, 32 = 2^5, 48 = 2^4 * 3^1.
Now, we need to take the highest exponent for each prime factor from the three numbers: The highest exponent of 2 is 5. The highest exponent of 3 is 1.
To calculate the LCM, we multiply the prime factors raised to their highest exponents: LCM = 2^5 * 3^1 = 32 * 3 = 96
Therefore, the LCM of 24, 32, and 48 is 96.
Jack needs to divide a number by 2 in order to get a product of 96. Which number should he use?
Jack should use 192 as his dividend since dividing it by 2 yields an answer of 96 (192 ÷ 2 = 96).
Diane needs to solve for X if 6x =96. What does X equal?
X equals 16 since solving for X yields 16 when 6x =96 (6x=96; x=16).
Harold needs to find out how many factors 96 has. How many factors does it have?
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Mike wants to find the prime factorization of 94. Can you tell him the prime factorization of 94
the prime factorization of 96 is 2^5 * 3.
Roy wants to determine if 15 and 19 are part of the list of factors for 94.
Let’s start with 15: 94 ÷ 15 = 6, remainder 4, Since 15 does not divide 94 evenly, it is not a factor of 94.
Now, let’s check 19: 94 ÷ 19 = 4 remainder 18 Similarly, 19 does not divide 94 evenly, so it is also not a factor of 94.
Therefore, neither 15 nor 19 are factors of 94.
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