110 LearnersLast updated on May 26th, 2025
Factors of 709
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 709, how they are used in real life, and tips to learn them quickly.
What are the Factors of 709?
The numbers that divide 709 evenly are known as factors of 709.
A factor of 709 is a number that divides the number without remainder.
The factors of 709 are 1 and 709.
Negative factors of 709: -1 and -709.
Prime factors of 709: 709.
Prime factorization of 709:709 is a prime number itself.
The sum of factors of 709: 1 + 709 = 710
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How to Find Factors of 709?
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 709. Since 709 is a prime number, it is only divisible by 1 and itself. Thus, the multiplication method yields the factors:
Step 1: Multiply 709 by 1, 709 × 1 = 709.
Therefore, the positive factor pair of 709 is: (1, 709).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with 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 709 by 1, 709 ÷ 1 = 709.
Step 2: Try dividing 709 by other numbers until the remainder becomes 0, but only 1 and 709 divide it evenly.
Therefore, the factors of 709 are: 1 and 709.
Prime Factors and Prime Factorization
The factors can be found by dividing it by prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, we find that 709 does not divide evenly by any prime numbers less than its square root, confirming it is prime itself.
Since 709 is a prime number, it is its own prime factor.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors.
However, for 709, as it is a prime number, the factor tree simply shows 709 as a single branch leading to itself.
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 709: (1, 709).
Negative factor pairs of 709: (-1, -709).
Common Mistakes and How to Avoid Them in Factors of 709
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 709, 1 and 709 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 709 consist of -1 and -709.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 709/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, 709 is a prime number, so its only factors are 1 and itself.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not recognizing 709 as a prime number and attempting unnecessary further factorization.
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Factors of 709 Examples
Problem 1
There are 709 apples in a crate. If a farmer wants to distribute them equally among 1 person, how many will each person get?
They will get 709 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
709/1 = 709
Problem 2
A flagpole is 709 meters tall. If you need to paint it using a ladder that can reach 1 meter at a time, how many climbs do you need to make?
709 climbs.
Explanation
To find the number of climbs, divide the height of the pole by the length each climb covers.
709/1 = 709
Problem 3
There are 709 pages in a book. If a reader plans to read 1 page a day, how many days will it take to complete the book?
709 days.
Explanation
To calculate the days needed, divide the total number of pages by pages read per day.
709/1 = 709
Problem 4
A concert hall has 1 entrance and has to accommodate 709 people. How many people will each entrance need to handle?
709 people.
Explanation
Divide the total number of people by the number of entrances.
709/1 = 709
Problem 5
709 items need to be packed into 1 box. How many items will each box contain?
Each box contains 709 items.
Explanation
Divide the total items by the number of boxes.
709/1 = 709
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FAQs on Factors of 709
1.What are the factors of 709?
2.Mention the prime factors of 709.
3.Is 709 a multiple of 1?
4.Mention the factor pairs of 709?
5.Is 709 a prime number?
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Important Glossaries for Factor of 709
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 709 are 1 and 709.
- Prime factors: The factors which are prime numbers. For example, 709 is a prime factor of itself.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 709 is (1, 709).
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 709 is a prime number.
- Negative factors: Factors that are negative counterparts of positive factors. For example, -1 and -709 are negative factors of 709.
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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.
