205 LearnersLast updated on May 26th, 2025
Factors of 343
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 343 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!
What are the factors of 343?
Factors are whole numbers that, when multiplied, the product is equal to 343.
343 is not a prime number, its factors are 1,7,49 and 343. For every factor, there is a corresponding negative factor, for 343, the negative factors -1, -7, -49 and -343.
How to find the factors of 343?
There are various methods we apply to find the factors of any number. Few of them are listed here; multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
Finding Factors Using Multiplication
Step 1: Find all pairs of numbers whose product is 343.
Step 2: All the pairs found represent the factors of 343.
343 is not a prime number. The pair of numbers whose product is 343 is;
1×343=343
7×49 = 343
The factors of 343 are 1, 7, 49 and 343.
Finding Factors by Division Method
Step 1: Start by dividing 343 with the smallest number, and check the remainders.
Step 2: 343 is not prime, therefore the divisors it has are 1, 7, 49 and 343. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 343 are 1, 7, 49 and 343.
Prime factors and prime factorization
— 343 is not a prime number.
— The prime factorization of 343 is 7×7×7 = 343.
— Factors of 343 are 1, 7, 49 and 343.
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its factors.
— In case of 343, only three branches will be extended as the number is prime factorized as 40 times 7 and 49 is factorized into 7 times 7. 7 is a prime number and cannot be factored further. The factorization ends here.
Common mistakes and how to avoid them in factors of 343
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 343. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them.
Mistake 1
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Factors of 343 Examples
Problem 1
Is 49 a factor of 343?
Divide 343 by 49: 343÷49=7.
Since 343 divides evenly by 49 (with no remainder), 49 is a factor of 343.
Explanation
To check if a number is a factor, divide the original number by it. If the division leaves no remainder, then it is a factor. Here, 49 divides 343 perfectly, so it is indeed a factor.
Problem 2
343 can be written as the product of 7 and another factor. What is the missing factor?
Divide 343 by 7: 343÷7=49
So, the missing factor is 49.
Explanation
To find a missing factor when you already know one factor, divide the number by the known factor. Here, dividing by 7 gives us the other factor, 49.
Problem 3
Find all the factors of 343.
Start with 1 (since 1 is a factor of every number).
Check each number up to the square root of 343 (about 18.5) to see if it divides evenly.
Dividing by 7: 343÷7=49, so both 7 and 49 are factors.
Dividing by 49: 343÷49=7, so we already have that factor pair.
Include 343 itself as a factor.
So, the factors of 343 are Find all the factors of 343.
Explanation
To find all factors, we only need to check up to the square root of 343, because factors repeat after that point. By testing each number up to 18.5, we identify the factors that divide 343 evenly without leaving a remainder.
FAQs on Factors of 343
1.Is 7 a factor of 343?
2.What is the GCF of 343?
3.Is 343 a perfect square number?
4.What is the triple root of 343?
5.Is 343 a perfect cube?
Important Glossaries for Factors of 343
- Factors: numbers that divide the given number without leaving a remainder.
- Prime factorization: breaking numbers down into their prime factors.
- Prime factors: Prime numbers that multiply together to form a given number.
- Composite number: Number that has at least more than one divisor other than 1 and the number itself.
Explore More numbers
Previous to Factors of 343
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.
