# Factors of 343

Factors of 343 are 1, 7, 49, and 343

#### How to find factors of a number

 1.   Find factors of 343 using Division Method 2.   Find factors of 343 using Prime Factorization 3.   Find factors of 343 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 343

• Divide 343 by 1: 343 ÷ 1 : Remainder = 0
• Divide 343 by 7: 343 ÷ 7 : Remainder = 0
• Divide 343 by 49: 343 ÷ 49 : Remainder = 0
• Divide 343 by 343: 343 ÷ 343 : Remainder = 0

Hence, Factors of 343 are 1, 7, 49, and 343

#### 2. Steps to find factors of 343 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 343 using the division method, follow these steps:

• Step 1. Start dividing 343 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 343, which is 7. Divide 343 by 7 to obtain the quotient (49).
343 ÷ 7 = 49
• Step 3. Repeat step 1 with the obtained quotient (49).
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 343 is, 343 = 7 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 343 as shown below:

So, the prime factorization of 343 is, 343 = 7 x 7 x 7.

#### 3. Find factors of 343 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 343 would be the two numbers which, when multiplied, give 343 as the result.

The following table represents the calculation of factors of 343 in pairs:

Factor Pair Pair Factorization
1 and 343 1 x 343 = 343
7 and 49 7 x 49 = 343

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 343. They are called negative pair factors.

Hence, the negative pairs of 343 would be ( -1 , -343 ) , ( -7 , -49 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 343 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 7, 49, 343 are exact divisors of 343.
• Factors of 343 are 1, 7, 49, 343. Each factor divides 343 without leaving a remainder.

• What are the prime factors of 343?

The factors of 343 are 1, 7, 49, 343.
Prime factors of 343 are 7, 7, 7.

• What is the sum of all factors of 343?

The sum of all factors of 343 is 400.

• What are the pair factors of 343?

Pair factors of 343 are (1,343), (7,49).

• What two numbers make 343?

Two numbers that make 343 are 7 and 49.

• What are multiples of 343?

First five multiples of 343 are 686, 1029, 1372, 1715.

• Is 343 a perfect square?

No 343 is not a perfect square.

• Which is greatest factor of 343?

The greatest factor of 343 is 49.

• How do you factors of 343?

Factors of 343 are 1, 7, 49, 343.

• What are five multiples of 343?

First five multiples of 343 are 686, 1029, 1372, 1715, 2058.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 343?

Factors of 343 are 1, 7, 49, 343.
Even factors of 343 are 0.
Hence, product of even factors of 343 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 343? Help her in writing all the factors.

Positive factors are 1, 7, 49, 343.
Negative factors are -1, -7, -49, -343.

How many factors are there for 343?

Factors of 343 are 1, 7, 49, 343.
So there are in total 4 factors.

Sammy is puzzled while calculating the prime factors of 343. Can you help him find them?

Factors of 343 are 1, 7, 49, 343.
Prime factors of 343 are 7, 7, 7

Joey wants to write all the prime factors of 343 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 343 are 7, 7, 7.
So in exponential form it can be written as 73.

What is prime factorization of 343?

Prime factorization of 343 is 7 x 7 x 7 = 73.

Can you help Rubel to find out the product of the even factors of 343?

Factors of 343 are 1, 7, 49, 343.
Even factors of 343 are 0.
Hence, product of even factors of 343 is; 0 = 0.