# Factors of 729 in pair

Factors of 729 in pair are (1, 729) , (3, 243) , (9, 81) and (27, 27)

#### How to find factors of a number in pair

 1.   Steps to find factors of 729 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 729 in pair

Factor Pair Pair Factorization
1 and 729 1 x 729 = 729
3 and 243 3 x 243 = 729
9 and 81 9 x 81 = 729
27 and 27 27 x 27 = 729

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 729. They are called negative pair factors.

Hence, the negative pairs of 729 would be ( -1 , -729 ) .

#### What does factor pairs of a number mean?

Factor pairs are those factors in pair that can give original number when multiplied. Every natural number is a product of atleast one factor pair. Eg- Factors of 729 are 1 , 3 , 9 , 27 , 81 , 243 , 729. So, factors of 729 in pair are (1,729), (3,243), (9,81), (27,27).

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of Factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 27, 81, 243, 729 are exact divisors of 729.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 729 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 729.

#### Steps to find Factors of 729

• Step 1. Find all the numbers that would divide 729 without leaving any remainder. Starting with the number 1 upto 364 (half of 729). The number 1 and the number itself are always factors of the given number.
729 ÷ 1 : Remainder = 0
729 ÷ 3 : Remainder = 0
729 ÷ 9 : Remainder = 0
729 ÷ 27 : Remainder = 0
729 ÷ 81 : Remainder = 0
729 ÷ 243 : Remainder = 0
729 ÷ 729 : Remainder = 0

Hence, Factors of 729 are 1, 3, 9, 27, 81, 243, and 729

• Is 729 a composite number?

Yes 729 is a composite number.

• Is 729 a perfect square?

Yes 729 is a perfect square.

• Write all odd factors of 729?

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

• What is the mean of all prime factors of 729?

Factors of 729 are 1 , 3 , 9 , 27 , 81 , 243 , 729. Prime factors of 729 are 3 , 3 , 3 , 3 , 3 , 3. Therefore mean of prime factors of 729 is (3 + 3 + 3 + 3 + 3 + 3) / 6 = 3.00.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

#### Examples of Factors

Can you help Rubel in arranging 729 blocks in order to form a rectangle in all possible ways? For arranging 729 blocks in order to form a rectangle in all possible ways we need to find factors of 729 in pair.

Factors of 729 are 1, 3, 9, 27, 81, 243, 729. So, factors of 729 in pair are (1,729), (3,243), (9,81), (27,27).

How many total number of factors of 729 in pair are possible?

Factors of 729 are 1, 3, 9, 27, 81, 243, 729. Hence, the factors of 729 in pair are (1,729), (3,243), (9,81), (27,27). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 729 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 729 are -1, -3, -9, -27, -81, -243, -729. Hence, factors of 729 in pair are (-1,-729), (-3,-243), (-9,-81), (-27,-27).

Find the product of all prime factors of 729.

Factors of 729 are 1, 3, 9, 27, 81, 243, 729. Prime factors are 3, 3, 3, 3, 3, 3. So, the product of all prime factors of 729 would be 3 x 3 x 3 x 3 x 3 x 3 = 729.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 729.
- Writing all prime factors of 729.
- Writing all the possible factors of 729 in pair.
Help him in writing all these.

Positive factors of 729 are 1, 3, 9, 27, 81, 243, 729.
Prime factors of 729 are 3, 3, 3, 3, 3, 3.
Factors of 729 in pair are (1,729), (3,243), (9,81), (27,27).

Can you help Sammy list the factors of 729 and also find the factor pairs?

Factors of 729 are 1, 3, 9, 27, 81, 243, 729.
Factors of 729 in pair are (1,729), (3,243), (9,81), (27,27).

Help Diji in finding factors of 729 by Prime Factorization method and then sorting factors of 729 in pairs.

Prime factorization of 729 is 3 x 3 x 3 x 3 x 3 x 3. Factors of 729 in pair can be written as (1,729), (3,243), (9,81), (27,27).

Write the smallest prime factor of 729.

Smallest prime factor of 729 is 3.