126 LearnersLast updated on May 26th, 2025
Factors of 1008
Factors are the numbers that divide any given number evenly without 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 1008, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1008?
The numbers that divide 1008 evenly are known as factors of 1008.
A factor of 1008 is a number that divides the number without remainder.
The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, and 1008.
Negative factors of 1008: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -16, -18, -21, -24, -28, -36, -42, -48, -56, -63, -72, -84, -112, -126, -144, -168, -252, -336, -504, and -1008.
Prime factors of 1008: 2, 3, and 7.
Prime factorization of 1008: 24 × 32 × 7.
The sum of factors of 1008: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 16 + 18 + 21 + 24 + 28 + 36 + 42 + 48 + 56 + 63 + 72 + 84 + 112 + 126 + 144 + 168 + 252 + 336 + 504 + 1008 = 3024
How to Find Factors of 1008?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1008. Identifying the numbers which are multiplied to get the number 1008 is the multiplication method.
Step 1: Multiply 1008 by 1, 1008 × 1 = 1008.
Step 2: Check for other numbers that give 1008 after multiplying:
2 × 504 = 1008
3 × 336 = 1008
4 × 252 = 1008
6 × 168 = 1008
7 × 144 = 1008
8 × 126 = 1008
9 × 112 = 1008
12 × 84 = 1008
14 × 72 = 1008
16 × 63 = 1008
18 × 56 = 1008
21 × 48 = 1008
24 × 42 = 1008
28 × 36 = 1008
Therefore, the positive factor pairs of 1008 are: (1, 1008), (2, 504), (3, 336), (4, 252), (6, 168), (7, 144), (8, 126), (9, 112), (12, 84), (14, 72), (16, 63), (18, 56), (21, 48), (24, 42), and (28, 36).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 1008 by 1, 1008 ÷ 1 = 1008.
Step 2: Continue dividing 1008 by the numbers until the remainder becomes 0.
1008 ÷ 1 = 1008
1008 ÷ 2 = 504
1008 ÷ 3 = 336
1008 ÷ 4 = 252
1008 ÷ 6 = 168
1008 ÷ 7 = 144
1008 ÷ 8 = 126
1008 ÷ 9 = 112
1008 ÷ 12 = 84
1008 ÷ 14 = 72
1008 ÷ 16 = 63
1008 ÷ 18 = 56
1008 ÷ 21 = 48
1008 ÷ 24 = 42
1008 ÷ 28 = 36
Therefore, the factors of 1008 are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1008 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.
1008 ÷ 2 = 504
504 ÷ 2 = 252
252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 1008 are 2, 3, and 7.
The prime factorization of 1008 is: 24 × 32 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1008 is divided by 2 to get 504.
Step 2: Now divide 504 by 2 to get 252.
Step 3: Then divide 252 by 2 to get 126.
Step 4: Divide 126 by 2 to get 63.
Step 5: Now divide 63 by 3 to get 21.
Step 6: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1008 is: 24 × 32 × 7.
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 1008: (1, 1008), (2, 504), (3, 336), (4, 252), (6, 168), (7, 144), (8, 126), (9, 112), (12, 84), (14, 72), (16, 63), (18, 56), (21, 48), (24, 42), and (28, 36).
Negative factor pairs of 1008: (-1, -1008), (-2, -504), (-3, -336), (-4, -252), (-6, -168), (-7, -144), (-8, -126), (-9, -112), (-12, -84), (-14, -72), (-16, -63), (-18, -56), (-21, -48), (-24, -42), and (-28, -36).
Common Mistakes and How to Avoid Them in Factors of 1008
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1008, 1 and 1008 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1008 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor because 1008/1.5 = 672, which is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1008 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 1008, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1008 as 24 × 32 × 7 and missing all the key factors.
Factors of 1008 Examples
Problem 1
There are 36 students and 1008 candies. How will they divide them equally?
They will get 28 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
1008/36 = 28
Problem 2
A garden is rectangular, the width of the garden is 12 meters and the total area is 1008 square meters. Find the length.
84 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1008 = length × 12
To find the value of length, we need to shift 12 to the left side.
1008/12 = length
Length = 84.
Problem 3
There are 21 baskets and 1008 apples. How many apples will be in each basket?
Each basket will have 48 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1008/21 = 48
Problem 4
In a drama club, there are 63 members, and 9 groups. How many members are there in each group?
There are 7 members in each group.
Explanation
Dividing the members by the total groups, we will get the number of members in each group.
63/9 = 7
Problem 5
1008 books need to be arranged in 84 shelves. How many books will go on each shelf?
Each of the shelves has 12 books.
Explanation
Divide total books by shelves.
1008/84 = 12
FAQs on Factors of 1008
1.What are the factors of 1008?
2.Mention the prime factors of 1008.
3.Is 1008 a multiple of 18?
4.Mention the factor pairs of 1008.
5.What is the square of 1008?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 1008?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 1008 with numbers?
8.What role do numbers and Factors of 1008 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 1008 skills?
Important Glossaries for Factor of 1008
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, and 1008.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 1008.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1008 are (1, 1008), (2, 504), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number.
- Division method: A method to find factors by dividing the original number by other numbers until the remainder is zero.
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About BrightChamps in United Arab Emirates
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
