Factors of 343
If a cube has 7 units as its dimension of its sides, then its volume of the cube is length × width × height = 7 × 7 × 7 = 343. Thus, we observe that 7 is a cube root of 343. In this lesson, we will calculate the factors of 343, prime factors of 343, and factors of 343 in pairs along with solved examples for a better understanding.
 Factors of 343: 1, 7, 49 and 343.
 Prime Factorization of 343: 7 × 7 × 7
1.  What Are the Factors of 343? 
2.  How to Calculate Factors of 343? 
3.  Factors of 343 by Prime Factorization 
4.  FAQs on Factors of 343 
What are the Factors of 343?
All the numbers that divide 343 completely leaving no remainder are the factors of 343. Factors of 343 are 1, 7, 49 and 343.
How to Calculate the Factors of 343?
Let's learn how to calculate factors of 343.
 1 is the factor of every number and the number itself is its factor. Thus we determine them as factors of 343.
 Find the number that completely divides 343. As 343 is not even, it is not divisible by any even number.
 Try the divisibility tests with 3, 5 and 10. It is not divisible by them.
 Check the divisibility with 7. 343 ÷ 7 = 49.
 We can stop here as 49 could be the only another factor. 343 ÷ 49 = 7
 Thus we determine the factors of 343 as 1× 343 and 7 × 49.
 This can be verified using the factor tree as well. The factor tree shows that 343 = 7 × 7 × 7. On getting the prime factors, we can determine all the possible composite factors of 343.
Explore factors using illustrations and interactive examples
 Factors of 512: The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
 Factors of 175: The factors of 175 are 1, 5, 7, 25, 35, 175.
 Factors of 49: The factors of 49 are 1, 7, and 49.
 Factors of 216: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216
 Factors of 112: The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
Factors of 343 by Prime Factorization
Factors of 343 by prime factorization are given by using the following steps. We can find the prime factors using the division method.
 Find the smallest prime number by which 343 can be divided without leaving any remainder.
 We see that 343 is divisible by 7.
 We can express 343 as 49 × 7.
 Again 49 can further be factorized as 7 × 7
 Therefore, prime factorization of 35 is 7 × 7 × 7 = 7 ^{3}
 Add 1 to the exponent thus obtained. Here the exponent is 3 and we conclude that there are 4 factors of 343 in all.
Factors of 343 in Pairs
The pair of numbers w multipled together gets the number 343 give the factors of 343 in pairs. 1 × 343, 7 × 49, 49 × 7 and 343 × 1 give the factors of 343 in pairs. The pair factors of 343 are:
 (1, 343)
 (7, 49)
 (49, 7)
 (343, 1)
Important Notes
 343 = 7 × 7 × 7 = 7^{3}. 343 is a perfect cube.
 7 is the prime factor of 343.
 1, 7, 49 and 343 are the distinct prime factors of 343.
Challenging Questions
 Find the 2 numbers that lie between 300 & 400 whose greatest common divisor is 49.
 Find the smallest integer n such that 49n becomes a cube number.
Factors of 343 Solved Examples

Example 1: She made 343 cookies which she has to distribute equally in tiny glass jars. If each jar can hold contain 7 cookies each, how many jars are needed?
Solution:
7 cookies × _____ jars = 343 cookies
7 × _____ = 343
To find the missing factor, we need to perform 343 ÷ 7
As, 343 ÷ 7 = 49
Therefore, she needs 49 jars 
Example 2: Jack is building a big cube with his tiny blocks. Jack lays 7 layers of 7 blocks for the base. How many such layers has he got to raise up if he has to complete the cube?
Solution: The number of blocks in the base built by Jack is 7 × 7 blocks = 49 blocks
49 × ____ = 343.
Finding the missing factor, 343 ÷ 49 = 7.
He raises the base with 7 such layers.
Thus, he builds up 7 layers of 7 × 7 blocks.
FAQs on Factors of 343
What are factors of 343?
The factors of 343 are 1, 7, 49 and 343
What are the common factors of 343 and 344?
 The factors of 343 are 1, 7, 49 and 343.
 The factors of 344 are 1, 2, 4, 8, 43, 86, 172 and 344
 The common factors of 343 and 344 is 1.
What are the factors of 343 that add up to 50?
The factors of 343 are 1, 7, 49 and 343. 49 + 1 = 50.
What are the common factors of 343 and 350?
 The factors of 343 are 1, 7, 49 and 343.
 The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350.
 The common factors of 343 and 350 are 1 and 7.
What are the prime factors of 343?
The distinct prime factor of 343 is 7.