Last updated on May 26th, 2025
Factors are 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 -68, how they are used in real life, and tips to learn them quickly.
The numbers that divide -68 evenly are known as factors of -68.
A factor of -68 is a number that divides the number without a remainder.
The positive factors of 68 are 1, 2, 4, 17, 34, and 68.
The negative factors of -68: -1, -2, -4, -17, -34, and -68.
Prime factors of 68: 2 and 17.
Prime factorization of 68: 2² × 17.
The sum of positive factors of 68: 1 + 2 + 4 + 17 + 34 + 68 = 126
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we identify the pairs of numbers that multiply to give 68. Identifying the numbers that are multiplied to get the number 68 is the multiplication method.
Step 1: Multiply 68 by 1, 68 × 1 = 68.
Step 2: Check for other numbers that give 68 after multiplying 2 × 34 = 68 4 × 17 = 68
Therefore, the positive factor pairs of 68 are: (1, 68), (2, 34), and (4, 17).
All these factor pairs result in 68.
For every positive factor, there is a negative factor.
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 68 by 1, 68 ÷ 1 = 68.
Step 2: Continue dividing 68 by the numbers until the remainder becomes 0.
68 ÷ 1 = 68
68 ÷ 2 = 34
68 ÷ 4 = 17
Therefore, the factors of 68 are: 1, 2, 4, 17, 34, 68.
The factors can be found by dividing it by prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 68 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.
68 ÷ 2 = 34
34 ÷ 2 = 17
17 ÷ 17 = 1
The prime factors of 68 are 2 and 17.
The prime factorization of 68 is: 2² × 17.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 68 is divided by 2 to get 34.
Step 2: Now divide 34 by 2 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 68 is: 2² × 17.
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 68: (1, 68), (2, 34), and (4, 17).
Negative factor pairs of -68: (-1, -68), (-2, -34), and (-4, -17).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 4 friends and 68 marbles. How will they divide them equally?
They will get 17 marbles each.
To divide the marbles equally, we need to divide the total marbles by the number of friends.
68/4 = 17
A garden is rectangular, the length of the garden is 17 meters, and the total area is 68 square meters. Find the width.
4 meters.
To find the width of the garden, we use the formula, Area = length × width 68 = 17 × width
To find the value of width, we need to shift 17 to the left side.
68/17 = width
Width = 4.
There are 2 baskets and 68 apples. How many apples will be in each basket?
Each basket will have 34 apples.
To find the apples in each basket, divide the total apples by the number of baskets.
68/2 = 34
In a class, there are 68 pencils, and 4 boxes. How many pencils are there in each box?
There are 17 pencils in each box.
Dividing the pencils by the total boxes, we will get the number of pencils in each box.
68/4 = 17
68 chairs need to be arranged in 2 rows. How many chairs will go in each row?
Each row has 34 chairs.
Divide total chairs by rows.
68/2 = 34
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.