115 LearnersLast updated on May 26th, 2025
Factors of 714
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 714, how they are used in real life, and tips to learn them quickly.
What are the Factors of 714?
The numbers that divide 714 evenly are known as factors of 714.
A factor of 714 is a number that divides the number without remainder.
The factors of 714 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 102, 119, 153, 238, 357, and 714.
Negative factors of 714: -1, -2, -3, -6, -7, -9, -14, -17, -18, -21, -34, -42, -51, -102, -119, -153, -238, -357, and -714.
Prime factors of 714: 2, 3, 7, and 17.
Prime factorization of 714: 2 × 3 × 7 × 17.
The sum of factors of 714: 1 + 2 + 3 + 6 + 7 + 9 + 14 + 17 + 18 + 21 + 34 + 42 + 51 + 102 + 119 + 153 + 238 + 357 + 714 = 1908.
How to Find Factors of 714?
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 714. Identifying the numbers which are multiplied to get the number 714 is the multiplication method.
Step 1: Multiply 714 by 1, 714 × 1 = 714.
Step 2: Check for other numbers that give 714 after multiplying
2 × 357 = 714
3 × 238 = 714
6 × 119 = 714
7 × 102 = 714
9 × 79.333 (not a factor)
17 × 42 = 714
21 × 34 = 714
Therefore, the positive factor pairs of 714 are: (1, 714), (2, 357), (3, 238), (6, 119), (7, 102), (17, 42), (21, 34).
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 a simple division method -
Step 1: Divide 714 by 1, 714 ÷ 1 = 714.
Step 2: Continue dividing 714 by the numbers until the remainder becomes 0.
714 ÷ 1 = 714
714 ÷ 2 = 357
714 ÷ 3 = 238
714 ÷ 6 = 119
714 ÷ 7 = 102
714 ÷ 9 = 79.
333 (not a factor)
714 ÷ 17 = 42
714 ÷ 21 = 34
Therefore, the factors of 714 are: 1, 2, 3, 6, 7, 17, 21, 34, 42, 102, 119, 238, 357, 714.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 714 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
714 ÷ 2 = 357
357 ÷ 3 = 119
119 ÷ 7 = 17
17 ÷ 17 = 1
The prime factors of 714 are 2, 3, 7, and 17.
The prime factorization of 714 is: 2 × 3 × 7 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 714 is divided by 2 to get 357.
Step 2: Now divide 357 by 3 to get 119.
Step 3: Then divide 119 by 7 to get 17.
Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 714 is: 2 × 3 × 7 × 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 714: (1, 714), (2, 357), (3, 238), (6, 119), (7, 102), (17, 42), (21, 34).
Negative factor pairs of 714: (-1, -714), (-2, -357), (-3, -238), (-6, -119), (-7, -102), (-17, -42), (-21, -34).
Common Mistakes and How to Avoid Them in Factors of 714
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 714, 1 and 714 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 714 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 9 is a factor of 714, because 714/9 = 79.333, and it 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 714 are prime numbers.
For example, 2, 3, 7, and 17 are the prime factors of 714, but it has other factors like 6, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 714 as 2 × 3 × 7 × 17 and missing all the key factors.
Factors of 714 Examples
Problem 1
There are 6 teams and 714 points. How will they divide the points equally?
Each team will get 119 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
714/6 = 119
Problem 2
A rectangular garden has a length of 17 meters and the total area is 714 square meters. Find the width?
42 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
714 = 17 × width
To find the value of width, we need to shift 17 to the left side.
714/17 = width
Width = 42.
Problem 3
There are 21 boxes and 714 marbles. How many marbles will be in each box?
Each box will have 34 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
714/21 = 34
Problem 4
In a conference, there are 714 participants and 7 groups. How many participants are there in each group?
There are 102 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
714/7 = 102
Problem 5
714 apples need to be arranged in 3 baskets. How many apples will go in each basket?
Each of the baskets will have 238 apples.
Explanation
Divide total apples by the number of baskets.
714/3 = 238
FAQs on Factors of 714
1.What are the factors of 714?
2.Mention the prime factors of 714.
3.Is 714 a multiple of 3?
4.Mention the factor pairs of 714?
5.What is the square of 714?
6.How can children in Qatar use numbers in everyday life to understand Factors of 714?
7.What are some fun ways kids in Qatar can practice Factors of 714 with numbers?
8.What role do numbers and Factors of 714 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 714 skills?
Important Glossaries for Factors of 714
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 714 are 1, 2, 3, 6, 7, 17, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 17 are prime factors of 714.
- 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 714 are (1, 714), (2, 357), etc.
- Factorization: The process of breaking down a number into its factors. For example, the factorization of 714 is 2 × 3 × 7 × 17.
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to give the number. For example, 714 is 2 × 357, showing 2 and 357 are factors.
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About BrightChamps in Qatar
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.
