Factors of 729

The numbers that divide 729 evenly are known as factors of 729.

A factor of 729 is a number that divides the number without remainder.

The factors of 729 are 1, 3, 9, 27, 81, 243, and 729.

Negative factors of 729: -1, -3, -9, -27, -81, -243, and -729.

Prime factors of 729: 3.

Prime factorization of 729: 3⁶

The sum of factors of 729: 1 + 3 + 9 + 27 + 81 + 243 + 729 = 1093

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
• Finding factors using division method
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 729. Identifying the numbers which are multiplied to get the number 729 is the multiplication method.

Step 1: Multiply 729 by 1, 729 × 1 = 729.

Step 2: Check for other numbers that give 729 after multiplying

3 × 243 = 729

9 × 81 = 729

27 × 27 = 729

Therefore, the positive factor pairs of 729 are: (1, 729), (3, 243), (9, 81), (27, 27).

All these factor pairs result in 729.

For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method 

Step 1: Divide 729 by 1, 729 ÷ 1 = 729.

Step 2: Continue dividing 729 by the numbers until the remainder becomes 0.

729 ÷ 1 = 729

729 ÷ 3 = 243

729 ÷ 9 = 81

729 ÷ 27 = 27

Therefore, the factors of 729 are: 1, 3, 9, 27, 81, 243, and 729.

The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 729 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

729 ÷ 3 = 243

243 ÷ 3 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factor of 729 is 3. The prime factorization of 729 is: 3⁶.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows 

Step 1: Firstly, 729 is divided by 3 to get 243.

Step 2: Now divide 243 by 3 to get 81.

Step 3: Then divide 81 by 3 to get 27.

Step 4: Divide 27 by 3 to get 9.

Step 5: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 729 is: 3⁶.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 729: (1, 729), (3, 243), (9, 81), and (27, 27).

Negative factor pairs of 729: (-1, -729), (-3, -243), (-9, -81), and (-27, -27).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 729 are 1, 3, 9, 27, 81, 243, and 729.

• Prime factors: The factors which are prime numbers. For example, 3 is a prime factor of 729.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 729 are (1, 729), (3, 243), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 729 is 3⁶.

• Negative factors: Factors that are negative, similar to positive factors but with a minus sign. For example, negative factors of 729 are -1, -3, -9, etc.