# Factors of 693

Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693

#### How to find factors of a number

 1.   Find factors of 693 using Division Method 2.   Find factors of 693 using Prime Factorization 3.   Find factors of 693 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 693

• Divide 693 by 1: 693 ÷ 1 : Remainder = 0
• Divide 693 by 3: 693 ÷ 3 : Remainder = 0
• Divide 693 by 7: 693 ÷ 7 : Remainder = 0
• Divide 693 by 9: 693 ÷ 9 : Remainder = 0
• Divide 693 by 11: 693 ÷ 11 : Remainder = 0
• Divide 693 by 21: 693 ÷ 21 : Remainder = 0
• Divide 693 by 33: 693 ÷ 33 : Remainder = 0
• Divide 693 by 63: 693 ÷ 63 : Remainder = 0
• Divide 693 by 77: 693 ÷ 77 : Remainder = 0
• Divide 693 by 99: 693 ÷ 99 : Remainder = 0
• Divide 693 by 231: 693 ÷ 231 : Remainder = 0
• Divide 693 by 693: 693 ÷ 693 : Remainder = 0

Hence, Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, and 693

#### 2. Steps to find factors of 693 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 693 using the division method, follow these steps:

• Step 1. Start dividing 693 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 693, which is 3. Divide 693 by 3 to obtain the quotient (231).
693 ÷ 3 = 231
• Step 3. Repeat step 1 with the obtained quotient (231).
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1

So, the prime factorization of 693 is, 693 = 3 x 3 x 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 693 as shown below:

So, the prime factorization of 693 is, 693 = 3 x 3 x 7 x 11.

#### 3. Find factors of 693 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 693 would be the two numbers which, when multiplied, give 693 as the result.

The following table represents the calculation of factors of 693 in pairs:

Factor Pair Pair Factorization
1 and 693 1 x 693 = 693
3 and 231 3 x 231 = 693
7 and 99 7 x 99 = 693
9 and 77 9 x 77 = 693
11 and 63 11 x 63 = 693
21 and 33 21 x 33 = 693

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 693. They are called negative pair factors.

Hence, the negative pairs of 693 would be ( -1 , -693 ) , ( -3 , -231 ) , ( -7 , -99 ) , ( -9 , -77 ) , ( -11 , -63 ) and ( -21 , -33 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693 are exact divisors of 693.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 693 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 693.

• Which is the smallest prime factor of 693?

Smallest prime factor of 693 is 3.

• Is 693 a perfect square?

No 693 is not a perfect square.

• What are five multiples of 693?

First five multiples of 693 are 1386, 2079, 2772, 3465, 4158.

• What is prime factorization of 693?

Prime factorization of 693 is 3 x 3 x 7 x 11.

• What are factors of 693?

Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.

• How do you find factors of a negative number? ( eg. -693 )?

Factors of -693 are -1, -3, -7, -9, -11, -21, -33, -63, -77, -99, -231, -693.

• Is 693 a whole number?

Yes 693 is a whole number.

• Which is greatest factor of 693?

The greatest factor of 693 is 231.

• What are the prime factors of 693?

The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
Prime factors of 693 are 3, 3, 7, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 693. Can you help her?

Prime factors of 693 are 3, 3, 7, 11.
Hence, the product of prime factors of 231.

Can you help Rubel to find out the product of the even factors of 693?

Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
Even factors of 693 are 0.
Hence, product of even factors of 693 is; 0 = 0.

Joy wants to calculate mean of all the factors of 693. Help him in finding the mean of 693.

Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 693 is 1 + 3 + 7 + 9 + 11 + 21 + 33 + 63 + 77 + 99 + 231 + 693 = 1248.
Hence, the mean of factors of 693 is 1248 ÷ 12 = 104.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 693? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
Negative factors are -1, -3, -7, -9, -11, -21, -33, -63, -77, -99, -231, -693.

How many factors are there for 693?

Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
So there are in total 12 factors.

Joey wants to write all the prime factors of 693 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 693 are 3, 3, 7, 11.
So in exponential form it can be written as 32 x 7 x 11.

Kevin has been asked to write 11 factor(s) of 693. Can you predict the answer?

11 factor(s) of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231.