# Factors of 726

Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726

#### How to find factors of a number

 1.   Find factors of 726 using Division Method 2.   Find factors of 726 using Prime Factorization 3.   Find factors of 726 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 726

• Divide 726 by 1: 726 ÷ 1 : Remainder = 0
• Divide 726 by 2: 726 ÷ 2 : Remainder = 0
• Divide 726 by 3: 726 ÷ 3 : Remainder = 0
• Divide 726 by 6: 726 ÷ 6 : Remainder = 0
• Divide 726 by 11: 726 ÷ 11 : Remainder = 0
• Divide 726 by 22: 726 ÷ 22 : Remainder = 0
• Divide 726 by 33: 726 ÷ 33 : Remainder = 0
• Divide 726 by 66: 726 ÷ 66 : Remainder = 0
• Divide 726 by 121: 726 ÷ 121 : Remainder = 0
• Divide 726 by 242: 726 ÷ 242 : Remainder = 0
• Divide 726 by 363: 726 ÷ 363 : Remainder = 0
• Divide 726 by 726: 726 ÷ 726 : Remainder = 0

Hence, Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726

#### 2. Steps to find factors of 726 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 726 using the division method, follow these steps:

• Step 1. Start dividing 726 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 726, which is 2. Divide 726 by 2 to obtain the quotient (363).
726 ÷ 2 = 363
• Step 3. Repeat step 1 with the obtained quotient (363).
363 ÷ 3 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1

So, the prime factorization of 726 is, 726 = 2 x 3 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 726 as shown below:

So, the prime factorization of 726 is, 726 = 2 x 3 x 11 x 11.

#### 3. Find factors of 726 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 726 would be the two numbers which, when multiplied, give 726 as the result.

The following table represents the calculation of factors of 726 in pairs:

Factor Pair Pair Factorization
1 and 726 1 x 726 = 726
2 and 363 2 x 363 = 726
3 and 242 3 x 242 = 726
6 and 121 6 x 121 = 726
11 and 66 11 x 66 = 726
22 and 33 22 x 33 = 726

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 726. They are called negative pair factors.

Hence, the negative pairs of 726 would be ( -1 , -726 ) , ( -2 , -363 ) , ( -3 , -242 ) , ( -6 , -121 ) , ( -11 , -66 ) and ( -22 , -33 ) .

#### 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. 726 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, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726 are exact divisors of 726.
• 1 is a factor of every number. Eg. 1 is a factor of 726.
• Every number is a factor of zero (0), since 726 x 0 = 0.

• How do you find factors of a negative number? ( eg. -726 )?

Factors of -726 are -1, -2, -3, -6, -11, -22, -33, -66, -121, -242, -363, -726.

• What is the sum of all factors of 726?

The sum of all factors of 726 is 1596.

• What is prime factorization of 726?

Prime factorization of 726 is 2 x 3 x 11 x 11.

• What are the pair factors of 726?

Pair factors of 726 are (1,726), (2,363), (3,242), (6,121), (11,66), (22,33).

• What are six multiples of 726?

First five multiples of 726 are 1452, 2178, 2904, 3630, 4356, 5082.

• Is 726 a whole number?

Yes 726 is a whole number.

• Which is the smallest prime factor of 726?

Smallest prime factor of 726 is 2.

• What are five multiples of 726?

First five multiples of 726 are 1452, 2178, 2904, 3630, 4356.

• Write all factors of 726?

Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.

#### Examples of Factors

Joey wants to write all the prime factors of 726 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 726 are 2, 3, 11, 11.
So in exponential form it can be written as 2 x 3 x 112.

How many factors are there for 726?

Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 726. Can you predict the answer?

11 factor(s) of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363.

Sammy is puzzled while calculating the prime factors of 726. Can you help him find them?

Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.
Prime factors of 726 are 2, 3, 11, 11

What is prime factorization of 726?

Prime factorization of 726 is 2 x 3 x 11 x 11 = 2 x 3 x 112.

Ariel has been assigned the task to find the product of all the prime factors of 726. Can you help her?

Prime factors of 726 are 2, 3, 11, 11.
Hence, the product of prime factors of 66.

Can you help Rubel to find out the product of the even factors of 726?

Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.
Even factors of 726 are 2, 6, 22, 66, 242, 726.
Hence, product of even factors of 726 is; 2 x 6 x 22 x 66 x 242 x 726 = 3061257408.