101 LearnersLast updated on May 27th, 2025
Factors of 672
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 672, how they are used in real life, and tips to learn them quickly.
What are the Factors of 672?
The numbers that divide 672 evenly are known as factors of 672.
A factor of 672 is a number that divides the number without a remainder.
The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, and 672.
Negative factors of 672: -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -32, -42, -48, -56, -84, -96, -112, -168, -224, -336, and -672.
Prime factors of 672: 2, 3, and 7.
Prime factorization of 672: 25 × 3 × 7.
The sum of factors of 672: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 32 + 42 + 48 + 56 + 84 + 96 + 112 + 168 + 224 + 336 + 672 = 2016.
How to Find Factors of 672?
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 672. Identifying the numbers which are multiplied to get the number 672 is the multiplication method.
Step 1: Multiply 672 by 1, 672 × 1 = 672.
Step 2: Check for other numbers that give 672 after multiplying
2 × 336 = 672
3 × 224 = 672
4 × 168 = 672
6 × 112 = 672
7 × 96 = 672
8 × 84 = 672
12 × 56 = 672
14 × 48 = 672
16 × 42 = 672
21 × 32 = 672
24 × 28 = 672
Therefore, the positive factor pairs of 672 are: (1, 672), (2, 336), (3, 224), (4, 168), (6, 112), (7, 96), (8, 84), (12, 56), (14, 48), (16, 42), (21, 32), and (24, 28).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 672 by 1, 672 ÷ 1 = 672.
Step 2: Continue dividing 672 by the numbers until the remainder becomes 0.
672 ÷ 1 = 672
672 ÷ 2 = 336
672 ÷ 3 = 224
672 ÷ 4 = 168
672 ÷ 6 = 112
672 ÷ 7 = 96
672 ÷ 8 = 84
672 ÷ 12 = 56
672 ÷ 14 = 48
672 ÷ 16 = 42
672 ÷ 21 = 32
672 ÷ 24 = 28
Therefore, the factors of 672 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 672 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
672 ÷ 2 = 336
336 ÷ 2 = 168
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 672 are 2, 3, and 7.
The prime factorization of 672 is: 25 × 3 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 672 is divided by 2 to get 336.
Step 2: Now divide 336 by 2 to get 168.
Step 3: Then divide 168 by 2 to get 84.
Step 4: Divide 84 by 2 to get 42.
Step 5: Divide 42 by 2 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 672 is: 25 × 3 × 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 672: (1, 672), (2, 336), (3, 224), (4, 168), (6, 112), (7, 96), (8, 84), (12, 56), (14, 48), (16, 42), (21, 32), and (24, 28).
Negative factor pairs of 672: (-1, -672), (-2, -336), (-3, -224), (-4, -168), (-6, -112), (-7, -96), (-8, -84), (-12, -56), (-14, -48), (-16, -42), (-21, -32), and (-24, -28).
Common Mistakes and How to Avoid Them in Factors of 672
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 672, 1 and 672 are also factors.
Factors of 672 Examples
Problem 1
A gardener has 672 flowers and wants to make bouquets with 8 flowers in each. How many bouquets can be made?
84 bouquets can be made.
Explanation
To divide the flowers equally, we need to divide the total flowers by the number of flowers per bouquet.
672/8 = 84
Problem 2
A rectangular playground has a length of 42 meters and a total area of 672 square meters. What is the width of the playground?
16 meters.
Explanation
To find the width of the playground, we use the formula, Area = length × width
672 = 42 × width
To find the value of width, we need to divide 672 by 42.
672/42 = width
Width = 16.
Problem 3
A baker has 672 cookies and 24 trays. How many cookies will be on each tray?
Each tray will have 28 cookies.
Explanation
To find the number of cookies on each tray, divide the total cookies by the number of trays.
672/24 = 28
Problem 4
In a class, there are 672 students, and they are being grouped into 7 teams. How many students are there in each team?
There are 96 students in each team.
Explanation
Dividing the students by the total number of teams will give the number of students in each team.
672/7 = 96
Problem 5
A library has 672 books that need to be arranged on 28 shelves. How many books will go on each shelf?
Each of the shelves has 24 books.
Explanation
Divide the total books by the number of shelves.
672/28 = 24
FAQs on Factors of 672
1.What are the factors of 672?
2.Mention the prime factors of 672.
3.Is 672 a multiple of 14?
4.Mention the factor pairs of 672?
5.What is the square of 672?
Important Glossaries for Factor of 672
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, and 672.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 672.
- 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 672 are (1, 672), (2, 336), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 672 is 25 × 3 × 7.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 672 is a multiple of 14.
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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.
