What Are the Factors of 343?
The factor of a number is a natural number that exactly divides the number, that is, the remainder after the division operation is zero. If two or more numbers are multiplied to obtain the product, the numbers being multiplied are called the factors of the product.
So as per the definition of ‘factors of a number’, the factors of 343 are the numbers that divide 343 evenly, leaving no remainder. So if ‘x’ is a factor of 343, then 343 is divisible by x, and if x is not a factor of 343, the dividing 343 by x leaves a finite remainder.
A factor of 343 is also defined as a number that can be multiplied by another number to give 343 as the product.
Finding Factors of 343
Let’s find the factors of 343 using the division operation.
Let’s consider an example:
7 is a factor of 343 because on dividing 343 by 7 we get zero as the remainder. The quotient, 49 is also a factor of 343.
Therefore, to check whether a number is a factor of 343, divide 343 by that number, if the remainder is zero, then, that number is said to be a factor of 343.
Prime Factors of 343
The number 343 is a composite number, that is, it has more than two factors. To carry out the prime factorization of 343, we will draw the factor tree of 343.
So the prime factorization of 343 is,
\(343 = 7 \times 7 \times 7.\)
Factor Pairs of 343
The factor pair of 434 is a set of two factors of 343 that when multiplied together give the product as 343. Factor pairs of a number can be listed from the set of factors of the number.
The factor pairs of 343 are: (1, 343) and (7, 49).
Solved Examples
Example 1: Find the common factors between 49 and 343.
Solution:
Factors of 49 = 1, 7, and 49.
Factors of 343 = 1, 7, 49 and 343.
Therefore, the common factors between 49 and 343 are 1, 7 and 49.
Example 2: Rex owns a bookstore. He decides to sort the books on the shelves such that there are an equal number of books on each shelf. The store has 343 books and 49 shelves. How can he place the books equally?
Solution:
\(343 \div 49 = 7 R0.\)
As 343 is a multiple of 49, we get 0 as the remainder.
Therefore, to arrange the books equally on the shelves, Rex would have to place 7 books on each shelf.
The factors of 343 are 1, 7, 49 and 343. So, the lowest factor of 343 is 1, and the highest factor of 343 is 343 itself.
On dividing 343 by 3 we get 1 as the remainder. So, 343 is not exactly divisible by 3, and thus 3 is not a factor of 343.
The negative factor pairs of 343 are (-1, -343) and (-7, -49).