# Factors of 686

Factors of 686 are 1, 2, 7, 14, 49, 98, 343, and 686

#### How to find factors of a number

 1.   Find factors of 686 using Division Method 2.   Find factors of 686 using Prime Factorization 3.   Find factors of 686 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 686

• Divide 686 by 1: 686 ÷ 1 : Remainder = 0
• Divide 686 by 2: 686 ÷ 2 : Remainder = 0
• Divide 686 by 7: 686 ÷ 7 : Remainder = 0
• Divide 686 by 14: 686 ÷ 14 : Remainder = 0
• Divide 686 by 49: 686 ÷ 49 : Remainder = 0
• Divide 686 by 98: 686 ÷ 98 : Remainder = 0
• Divide 686 by 343: 686 ÷ 343 : Remainder = 0
• Divide 686 by 686: 686 ÷ 686 : Remainder = 0

Hence, Factors of 686 are 1, 2, 7, 14, 49, 98, 343, and 686

#### 2. Steps to find factors of 686 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 686 using the division method, follow these steps:

• Step 1. Start dividing 686 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 686, which is 2. Divide 686 by 2 to obtain the quotient (343).
686 ÷ 2 = 343
• Step 3. Repeat step 1 with the obtained quotient (343).
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 686 is, 686 = 2 x 7 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 686 as shown below:

So, the prime factorization of 686 is, 686 = 2 x 7 x 7 x 7.

#### 3. Find factors of 686 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 686 would be the two numbers which, when multiplied, give 686 as the result.

The following table represents the calculation of factors of 686 in pairs:

Factor Pair Pair Factorization
1 and 686 1 x 686 = 686
2 and 343 2 x 343 = 686
7 and 98 7 x 98 = 686
14 and 49 14 x 49 = 686

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 686. They are called negative pair factors.

Hence, the negative pairs of 686 would be ( -1 , -686 ) , ( -2 , -343 ) , ( -7 , -98 ) and ( -14 , -49 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 686 is a factor of itself.
• 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, 2, 7, 14, 49, 98, 343, 686 are exact divisors of 686.
• 1 is a factor of every number. Eg. 1 is a factor of 686.
• Every number is a factor of zero (0), since 686 x 0 = 0.

• What two numbers make 686?

Two numbers that make 686 are 2 and 343.

• What is prime factorization of 686?

Prime factorization of 686 is 2 x 7 x 7 x 7.

• Write some multiples of 686?

First five multiples of 686 are 1372, 2058, 2744, 3430.

• Which is the smallest prime factor of 686?

The smallest prime factor of 686 is 2.

• Is 686 a perfect square?

No 686 is not a perfect square.

• What is the sum of all factors of 686?

The sum of all factors of 686 is 1200.

• What are factors of 686?

Factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686.

• How do you find factors of a negative number? ( eg. -686 )?

Factors of -686 are -1, -2, -7, -14, -49, -98, -343, -686.

• Is 686 a whole number?

Yes 686 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 686. Help him in finding the mean of 686.

Factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 686 is 1 + 2 + 7 + 14 + 49 + 98 + 343 + 686 = 1200.
Hence, the mean of factors of 686 is 1200 ÷ 8 = 150.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 686? Help her in writing all the factors.

Positive factors are 1, 2, 7, 14, 49, 98, 343, 686.
Negative factors are -1, -2, -7, -14, -49, -98, -343, -686.

Joey wants to write all the prime factors of 686 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 686 are 2, 7, 7, 7.
So in exponential form it can be written as 2 x 73.

Kevin has been asked to write 7 factor(s) of 686. Can you predict the answer?

7 factor(s) of 686 are 1, 2, 7, 14, 49, 98, 343.

Sammy is puzzled while calculating the prime factors of 686. Can you help him find them?

Factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686.
Prime factors of 686 are 2, 7, 7, 7

What is prime factorization of 686?

Prime factorization of 686 is 2 x 7 x 7 x 7 = 2 x 73.

Can you help Rubel to find out the product of the even factors of 686?

Factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686.
Even factors of 686 are 2, 14, 98, 686.
Hence, product of even factors of 686 is; 2 x 14 x 98 x 686 = 1882384.