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Factors of 96 are the natural numbers that can divide the original number 96 without leaving any remainder. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96 are the factors of 96. The factors of 96 leave a whole number as the quotient on dividing 96. 96 has a total of 12 factors of which 96 is the biggest factor. The prime factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3 or 25 × 3. Thus, there are only two prime factors of 96 which are 2 and 3. The pair factors of 96 are (1,96), (2,48), (3,32), (4,24), (6,16), and (8,12).
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Key Terms: Factors of 96, Remainder, Prime Factors, Prime Factorization, Pair Factors, Prime Numbers, Composite Number
What are Factors of 96?
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Factors of 96 are numbers that, when multiplied in pairs, produce the number 96 as the product. The number 96 is a composite number and has a total of 12 factors of which 96 is the largest factor and 2 and 3 are the only prime factors.
| Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 |
- Negative Factors of 96: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48 and -96
- Prime Factors of 96: 2, 3
- Prime Factorization of 96: 2 × 2 × 2 × 2 × 2 × 3 = 25 × 3
- Sum of Factors of 96: 252
![factor of 96]()
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Factors of 96 in Pairs
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The numbers that are multiplied together in pairs to give the original number 96 are called the pair factors of 96. A number can have both positive and negative pair factors.
The positive and negative pair factors of 96 are as follows:
| Positive Pair Factors of 96 | Negative Pair Factors of 96 |
|---|---|
| 1 × 96 = 96 (1, 96) | -1 × -96 = 96 (-1, -96) |
| 2 × 48 = 96 (2, 48) | -2 × -48 = 96 (-2, -48) |
| 3 × 32 = 96 (3, 32) | -3 × -32 = 96 (-3, -32) |
| 4 × 24 = 96 (4, 24) | -4 × -24 = 96 (-4, -24) |
| 6 × 16 = 96 (6, 16) | -6 × -16 = 96 (-6, -16) |
| 8 × 12 = 96 ( 8, 12) | -8 × -12 = 96 (-8, -12) |
How to Calculate Factors of 96?
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In order to find the factors of 96, we need to check which numbers divide 96 completely without leaving any remainder. Every number, be it a prime number or a composite number, has two factors which are 1 and the number itself. Thus, all the factors of a particular number lie between 1 and the number itself.
- 96 ÷ 1 = 96 ( Remainder is 0)
- 96 ÷ 2 = 48 (Remainder is 0)
- 96 ÷ 3 = 32 (Remainder is 0)
- 96 ÷ 4 = 24 (Remainder is 0)
- 96 ÷ 6 = 16 (Remainder is 0)
- 96 ÷ 8 = 12 (Remainder is 0)
- 96 ÷ 12 = 8 (Remainder is 0)
- 96 ÷ 16 = 6 (Remainder is 0)
- 96 ÷ 24 = 4 (Remainder is 0)
- 96 ÷ 32 = 3 (Remainder is 0)
- 96 ÷ 48 = 2 (Remainder is 0)
- 96 ÷ 96 = 1 (Remainder is 0)
Therefore, the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Read More: HCF of Two Numbers
Prime Factorization of 96
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Prime factorization gives the prime factors of a particular number. It is a method of expressing a number as the product of its prime factors. The prime factorization of 96 is as follows:
Step 1: Divide 96 by the smallest prime factor, say 2.
96 ÷ 2 = 48
Step 2: Continue the division until the number cannot be divided by 2 further or you get 1 at the end.
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
Step 3: We know that 3 is not divisible by 2, so, we will move on with the next prime number which is 3.
3 ÷ 3 = 1
Since, we have received 1 at the end of the division process, we will not proceed further. Thus, the prime factorization of 96 is 2 x 2 x 2 x 2 x 2 x 3 or 25 x 3, with 2 and 3 as the only prime factors of 96.
Read More: Greatest Common Divisor
Factor Tree of 96
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Factor tree of 96 provides the pictorial representation of the factors of 96. The endpoints of the factor tree denote the prime factors of 96. Factor Tree of 96 is as follows:
Solved Examples on Factors of 96
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Here are a few solved examples on the factors of 96:
| Example 1: Find the Greatest Common Factor of 96 and 19. Solution: First, we will list all the factors of 96 and 19,
Thus, there is only one common factor of 96 and 19 which is 1. Therefore, the Greatest Common Factor (GCF) of 96 and 19 is 1. Example 2: Find the average of the factors of 96. Solution: We know that the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. Average = Sum of all Factors ÷ Total Number of Factors Average of Factors of 96 = (1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96) ÷ 12 Average of Factors of 96 = 252 ÷ 12 = 21 Thus, the average of the factors of 96 is 21. |
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Things to Remember
- Factors of 96 are the natural numbers that divide 96 completely leaving zero as the remainder.
- 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96 are the 12 factors of 96.
- The pair factors of 96 are (1,96), (2,48), (3, 32), (4, 24), (6,16), and (8, 12).
- 96 has two prime factors namely 2 and 3.
- The prime factorization of 96 is 25 × 3.
- The sum of the factors of 96 is 252.
Sample Questions
Ques. What is the sum of the factors of 96? (2 Marks)
Ans. The number 96 has 12 factors in total. Adding them up, we get
1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96 = 126
Therefore, 252 is the sum of all the factors of 96.
Ques. What are the multiples of 96? (2 Marks)
Ans. Multiples of 96 are the number obtained as the product when 96 is multiplied by an integer. A number can have infinite multiples. The first 10 multiples of 96 are as follows:
- 96 × 1 = 96
- 96 × 2 = 192
- 96 × 3 = 288
- 96 × 4 = 384
- 96 × 5 = 480
- 96 × 6 = 576
- 96 × 7 = 672
- 96 × 8 = 768
- 96 × 9 = 864
- 96 × 10 = 960
Ques. What is a Factor? (2 Marks)
Ans. A factor is a number that divides another number, without leaving a remainder. A number can have a finite number of factors only. For example, 2 is a factor of 24 as it divided 24 completely without leaving any remainder.
Ques. Write the prime factorization of 96. (2 Marks)
Ans. The prime factorization of 96 can be written as
96 = 2 x 2 x 2 x 2 x 2 x 3
It can be simplified and written as 25 × 3.
Ques. Write the factors of 96 in ascending order. (2 Marks)
Ans. The factors of 68 in ascending order are as follows:
1 < 2 < 3 < 4 < 6 < 8 < 12 < 16 < 24 < 32 < 48 < 96
As per the arrangement, the smallest factor of 96 is 1 and the largest factor of 96 is 96.
Ques. What are the pair factors of 96? (2 Marks)
Ans. Pair factors of 96 are the pair of two numbers that give 96 as the product when multiplied by each other.
- 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
Therefore, factors of 96 in pairs are (1,96), (2,48), (3, 32), (4, 24), (6,16), and (8, 12).
Ques. What are the properties of factors of a number? (3 Marks)
Ans. The properties of factors of a given number are as mentioned below:
- Each natural number has a factor of itself.
- 1 is a factor of every number.
- A number’s factors are all less than or equal to the original value.
- Multiplication and division are two methods to find factors of a number.
- Except for 0 and 1, all whole numbers have at least two factors.
- Every number has a finite number of factors.
Ques. Are the factors and prime factors of 96 the same? (3 Marks)
Ans. Factors and prime factors of every number are different.
- Factors of 96 are all the numbers that can divide 96 completely, be it a prime number or a composite number. Thus, the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
- Prime Factors of 96 are the prime numbers that divide 96 completely. Thus, 2 and 3 are the prime factors of 96.
Ques. State some important facts about Factors of 96. (3 Marks)
Ans. Some important facts about factors of 96 are as follows:
- 96 is a composite number, thus, it has more than two factors.
- 2 and 3 are the only factors of 96.
- A number has finite factors, thus, 96 has a total of 12 factors only.
Ques. What is the product of all the prime factors of 96? (1 Mark)
Ans. The number 96 has only two prime factors which are 2, and 3. The product of prime factors of 96 is given as
2 × 3 = 6.
Thus, the product of prime factors of 96 is 6.
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