231 LearnersLast updated on May 26th, 2025
Factors of 192
Factors of 192 are numbers that help 192 to get divided evenly. Factors can be used to schedule time intervals in everyday life.
What are the Factors of 192
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192.
Negative Factors: These are negative counterparts for each positive factor.
Negative factors: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -192.
Prime Factors: Prime factors are the prime numbers themselves, and when multiplied together, they give 168 as the product.
Prime factor: 2,3
Prime Factorization: Prime factorization involves breaking 192 into its prime factors and expressing their product in exponential form.
It is expressed as 26 × 31
How to Find the Factors of 192
Listed below are the different methods that can be used to find the factors of 192.
Methods to find the factors of 192:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair factors that give 192 as their product. Here’s a step-by-step process to follow:
Step 1: Find the pair of numbers whose product is 192.
Step 2: These numbers are called the factor pairs.
Step 3: Make a list of numbers whose product will be 192.
A list of numbers whose products are 192 is given below:
1 × 192 = 192
2 × 96 = 192
3 × 64 =192
4 × 48 = 192
6 × 32 = 192
8 × 24 = 192
12 × 16= 192
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number and gives zero as the remainder. Here’s a step-by-step process of the method:
Step 1: Number 1 will always be a factor because we can divide any number by 1. Example: 192÷1 = 192
Step 2: Move to the next integer. Both divisor and quotient are the factors.
Overview of Factors of 192 using the division method
Prime Factors and Prime Factorization
Prime factors are the prime numbers, having 1 and the numbers themselves as factors. Prime factorization is breaking down the number into its prime factors and expressing their product using exponents.
Prime Factors of 192: There are two prime factors of 192
Prime factors of 192: 2,3
Follow the steps given below to find the prime factors of 192
Step 1: Divide 192 using the prime number 2
192÷2 = 96
96÷2 = 48
48÷2 = 24
24÷2 = 12
12÷2 = 6
6÷2 = 3
Step 2: Divide 3 with the prime number 3
3÷3 = 1
So, the prime Factorization expresses the product of prime numbers in its exponential form
Expressed as 26 × 31
Factor Tree
The prime factorization is visually represented using the factor tree. In this factor tree, each branch splits into prime factors.
Factor Pairs
Factor pairs of 192 are a team of 2 factors each. Their product will be equal to the number given.
Positive Factor Pairs: (1,192), (2,96), (3,64), (4,48), (6,32), (8,24), (12,16)
Negative Factor Pairs: (-1, -192), (-2, -96), (-3, -64), (-4, -48), (-6, -32),
(-8, -24), (-12, -16)
Common Mistakes and How to Avoid Them in Factors of 192
Students can make mistakes while finding the factors of 192 and the solutions to avoid those mistakes are given below.
Mistake 1
Using the subtraction sign ‘-’ instead of the division ‘÷’ sign
The subtraction sign‘-’ is used to take the difference between two numbers, and the division sign is used to divide the given number by another number (divisor) without any remainder. The use of the subtraction sign ‘-’ in the division method will give you incorrect results. Before you start the division process, check the sign twice and make sure you are using the correct sign.
Factors of 192 Examples
Problem 1
Can you identify the positive factors of 192 which are also multiples of 8?
The positive factors of 192 which are also multiples of 8 are 8, 16, 24, 32, 56, 64, and 96
Explanation
The multiples of 8 are numbers we get when 8 gets multiplied by another number. The multiples of 8 from the factor list of 192 are 8, 16, 24, 32, 56, 64, and 96
Problem 2
Find a perfect cube factor from the factors of 192
8 is the only perfect cube factor of 192
Explanation
A cube is a number we get when the same number is multiplied three times. Here, if we take factor 2 and multiply it three times, we have 8 as a perfect cube, which is also a factor of 192.
Problem 3
Find the product of all odd factors of 192
The product of odd factors is 3
Explanation
1 and 3 are the only odd factors of 192, while other factors are even.
The product we get is 3 (1×3)
FAQs on Factors of 192
1.What numbers are the factors of 192
2.The negative factor pairs of 192
3.Is 192 a prime number?
4.How many factors does 192 have?
5.What is the greatest factor of 192?
Important Glossaries for Factors of [Topic]
- Divisor: Number that divides another number
- Quotient: It is the number that gets as a result of division
- Factors: Numbers that divide the given number completely without any remainder.
- Prime Factors: Prime numbers that multiply together to form the given number.
- Prime Factorization: Process of breaking down the number into prime factors
- Negative Factors: These are the negative counterparts of the positive factor
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