# Factors of 711

Factors of 711 are 1, 3, 9, 79, 237, and 711

#### How to find factors of a number

 1.   Find factors of 711 using Division Method 2.   Find factors of 711 using Prime Factorization 3.   Find factors of 711 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 711

• Divide 711 by 1: 711 ÷ 1 : Remainder = 0
• Divide 711 by 3: 711 ÷ 3 : Remainder = 0
• Divide 711 by 9: 711 ÷ 9 : Remainder = 0
• Divide 711 by 79: 711 ÷ 79 : Remainder = 0
• Divide 711 by 237: 711 ÷ 237 : Remainder = 0
• Divide 711 by 711: 711 ÷ 711 : Remainder = 0

Hence, Factors of 711 are 1, 3, 9, 79, 237, and 711

#### 2. Steps to find factors of 711 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 711 using the division method, follow these steps:

• Step 1. Start dividing 711 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 711, which is 3. Divide 711 by 3 to obtain the quotient (237).
711 ÷ 3 = 237
• Step 3. Repeat step 1 with the obtained quotient (237).
237 ÷ 3 = 79
79 ÷ 79 = 1

So, the prime factorization of 711 is, 711 = 3 x 3 x 79.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 711 as shown below:

So, the prime factorization of 711 is, 711 = 3 x 3 x 79.

#### 3. Find factors of 711 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 711 would be the two numbers which, when multiplied, give 711 as the result.

The following table represents the calculation of factors of 711 in pairs:

Factor Pair Pair Factorization
1 and 711 1 x 711 = 711
3 and 237 3 x 237 = 711
9 and 79 9 x 79 = 711

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 711. They are called negative pair factors.

Hence, the negative pairs of 711 would be ( -1 , -711 ) , ( -3 , -237 ) and ( -9 , -79 ) .

#### 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

• Every number is a factor of zero (0), since 711 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, 3, 9, 79, 237, 711 are exact divisors of 711.
• Factors of 711 are 1, 3, 9, 79, 237, 711. Each factor divides 711 without leaving a remainder.

• Which is the smallest prime factor of 711?

Smallest prime factor of 711 is 3.

• Is 711 a perfect square?

No 711 is not a perfect square.

• What are five multiples of 711?

First five multiples of 711 are 1422, 2133, 2844, 3555, 4266.

• What is prime factorization of 711?

Prime factorization of 711 is 3 x 3 x 79.

• What are factors of 711?

Factors of 711 are 1, 3, 9, 79, 237, 711.

• How do you find factors of a negative number? ( eg. -711 )?

Factors of -711 are -1, -3, -9, -79, -237, -711.

• Is 711 a whole number?

Yes 711 is a whole number.

• Which is greatest factor of 711?

The greatest factor of 711 is 237.

• What are the prime factors of 711?

The factors of 711 are 1, 3, 9, 79, 237, 711.
Prime factors of 711 are 3, 3, 79.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 711. Can you help her?

Prime factors of 711 are 3, 3, 79.
Hence, the product of prime factors of 237.

Can you help Rubel to find out the product of the even factors of 711?

Factors of 711 are 1, 3, 9, 79, 237, 711.
Even factors of 711 are 0.
Hence, product of even factors of 711 is; 0 = 0.

Joy wants to calculate mean of all the factors of 711. Help him in finding the mean of 711.

Factors of 711 are 1, 3, 9, 79, 237, 711.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 711 is 1 + 3 + 9 + 79 + 237 + 711 = 1040.
Hence, the mean of factors of 711 is 1040 ÷ 6 = 173.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 711? Help her in writing all the factors.

Positive factors are 1, 3, 9, 79, 237, 711.
Negative factors are -1, -3, -9, -79, -237, -711.

How many factors are there for 711?

Factors of 711 are 1, 3, 9, 79, 237, 711.
So there are in total 6 factors.

Joey wants to write all the prime factors of 711 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 711 are 3, 3, 79.
So in exponential form it can be written as 32 x 79.

Kevin has been asked to write 5 factor(s) of 711. Can you predict the answer?

5 factor(s) of 711 are 1, 3, 9, 79, 237.