Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -192, how they are used in real life, and tips to learn them quickly.
The numbers that divide -192 evenly are known as factors of -192.
A factor of -192 is a number that divides the number without a remainder.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.
Negative factors of -192: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, and -192.
Prime factors of 192: 2 and 3.
Prime factorization of 192: 26 × 3.
The sum of factors of 192: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 192 = 511
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 192. Identifying the numbers which are multiplied to get the number 192 is the multiplication method.
Step 1: Multiply 192 by 1, 192 × 1 = 192.
Step 2: Check for other numbers that give 192 after multiplying 2 × 96 = 192 3 × 64 = 192 4 × 48 = 192 6 × 32 = 192 8 × 24 = 192 12 × 16 = 192
Therefore, the positive factor pairs of 192 are: (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), (12, 16).
For every positive factor, there is a negative factor.
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated using the simple division method:
Step 1: Divide 192 by 1, 192 ÷ 1 = 192.
Step 2: Continue dividing 192 by the numbers until the remainder becomes 0.
192 ÷ 1 = 192
192 ÷ 2 = 96
192 ÷ 3 = 64
192 ÷ 4 = 48
192 ÷ 6 = 32
192 ÷ 8 = 24
192 ÷ 12 = 16
Therefore, the factors of -192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
The factors can be found by dividing them by prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 192 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
192 ÷ 2 = 96
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
The prime factors of 192 are 2 and 3.
The prime factorization of 192 is: 2^6 × 3.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 192 is divided by 2 to get 96.
Step 2: Now divide 96 by 2 to get 48.
Step 3: Then divide 48 by 2 to get 24.
Step 4: Continue dividing by 2 until you reach the prime number 3. So, the prime factorization of 192 is: 26 × 3.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 192: (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), (12, 16).
Negative factor pairs of -192: (-1, -192), (-2, -96), (-3, -64), (-4, -48), (-6, -32), (-8, -24), (-12, -16).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A bookshelf has -192 books, and each shelf can hold 16 books. How many shelves are needed?
12 shelves are needed.
To determine the number of shelves needed, divide the total books by the books per shelf.
192/16 = 12
A rectangular ice rink has a length of 32 meters, and the total area is -192 square meters. Find the width.
6 meters.
To find the width of the ice rink, we use the formula,
Area = length × width
192 = 32 × width
To find the value of width, divide the area by the length.
192/32 = width Width = 6
There are 24 boxes and -192 candies. How many candies will be in each box?
Each box will have 8 candies.
To find the candies in each box, divide the total candies by the boxes.
192/24 = 8
In a school, there are -192 students, and 8 groups. How many students are there in each group?
There are 24 students in each group.
Dividing the students by the total groups will give the number of students in each group.
192/8 = 24
-192 flyers need to be distributed in 12 locations. How many flyers will go to each location?
Each location will receive 16 flyers.
Divide the total flyers by the number of locations.
192/12 = 16
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.