Factors of 711

The factors of 711 are the numbers that divide 711 evenly.

Positive Factors: These are positive integers that divide 711 completely.

Positive factors: 1, 3, 9, 79, 237, 711

Negative Factors: These are negative counterparts of the positive factors.

Negative factors: -1, -3, -9, -79, -237, -711

Prime Factors: Prime factors are the prime numbers that, when multiplied together, give 711 as the product.
Prime factors: 3, 79

Prime Factorization: Prime factorization involves breaking 711 into its prime factors.

It is expressed as 3²×79.

Table Listing the Factors of 711

This breakdown helps in understanding the various factors of 711, whether they are positive or negative, as well as how prime factorization works for this number.

There are different methods to find the factors of 711.

Methods to find the factors of 711:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

The multiplication method finds the pair of factors that give 711 as their product.

Find the pair of numbers whose product is 711.

The factors are those numbers that, when multiplied, give 711.

Make a list of numbers whose product equals 711.

A list of numbers whose products are 711 is given below:

• 1×711=711
• 3×237=711
• 9×79=711

Thus, the factors of 711 are 1, 3, 9, 79, 237, and 711.
 

The division method finds the numbers that fully divide the given number. The steps are given below:

Since every number is divisible by 1, 1 will always be a factor.

Example: 711÷1=711.

Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.

Thus, the factors of 711 are 1, 3, 9, 79, 237, and 711.
 

Multiplying prime numbers to get the given number as their product is called prime factors. A number, when it is simplified using the factors of that number and expressed in the form of prime factors, is the prime factorization of a number.

Prime Factors of 711: Number 711 has two prime factors.

Prime factors of 711: 3, 79

To find the prime factors of 711, we can divide 711 with prime numbers like 3 and 79 from the list of factors of 711.

Divide 711 with the prime number 3:

• 711÷3=237

Divide 237 with the prime number 3:

• 237÷3=79

79 is already a prime number.

Prime Factorization of 711:

• Expressed as 3²×79.

The prime factorization is visually represented using the factor tree. It helps to understand the process easily.

This tree shows the breakdown of 711 into its prime factors: 3×3×79.

Positive and Negative Factor Pairs of 711

Factors of 711 can be written in both positive pairs and negative pairs. Their product will be equal to the number given.

Positive Factor Pairs: (1, 711), (3, 237), (9, 79)

Negative Factor Pairs: (-1, -711), (-3, -237), (-9, -79)

• Factors: Numbers that can divide a given number completely without leaving a remainder. For example, 1, 3, 9, 79, 237, and 711 are factors of 711.

• Prime Factors: Prime numbers that, when multiplied together, give the original number. For 711, the prime factors are 3 and 79.

• Prime Factorization: The process of breaking a number into its prime factors. For 711, the prime factorization is expressed as 32×793^2 \times 7932×79.

• Factor Tree: A diagram that visually represents the breakdown of a number into its prime factors. It helps illustrate the process of finding the prime factorization.

• Perfect Square: A number that is the product of an integer multiplied by itself. The perfect square factor of 711 is 9 (since 3×3=93 \times 3 = 93×3=9).